AP Physics 1 flashcards

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Unit 1: Kinematics

1. Topic 1.1 · Say it in contextRight is positive. A cart moves left at 4 m/s. What are its velocity and its speed?

   Velocity is $-4$ m/s: the sign gives the direction in one dimension. Speed is 4 m/s, because speed is a scalar with magnitude only.

   Review: 1.1 Scalars and Vectors in One Dimension

2. Topic 1.2 · Spot the mistake"A car going around a curve at a steady 15 m/s is not accelerating." Is that right?

   No. An object accelerates whenever the magnitude or the direction of its velocity changes. On the curve the direction changes, so the car is accelerating even though its speed is constant.

   Review: 1.2 Displacement, Velocity, and Acceleration

3. Topic 1.2 · Work it outRight is positive. A ball's velocity changes from $+6$ m/s to $-4$ m/s in 2 s. Find its average acceleration.

   $a_{avg}=\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}=\frac{-4-6}{2}=-5{\text{m/s}}^2$. The negative sign means the average acceleration points left.

   Review: 1.2 Displacement, Velocity, and Acceleration

4. Topic 1.2 · Know the termWhat does it mean to use the object model for a car?

   You ignore the car's size, shape and internal parts and treat it as a single point that carries properties such as its mass.

   Review: 1.2 Displacement, Velocity, and Acceleration

5. Topic 1.3 · Say it in contextWhat does the slope of a tangent line on a position-time graph tell you, and what does a flat spot mean?

   The slope is the instantaneous velocity at that moment. A flat (zero-slope) spot means the object is momentarily at rest.

   Review: 1.3 Representing Motion

6. Topic 1.3 · Say it in contextOn a velocity-time graph, what does the area between the curve and the time axis give, and what does area below the axis mean?

   The area gives the displacement over that interval. Area below the axis counts as negative: the object moved in the negative direction during that time.

   Review: 1.3 Representing Motion

7. Topic 1.3 · Check the conditionsWhat must be true before you use $x=x_0+v_{x0}t+\frac{1}{2}{a}_x{t}^2$?

   The acceleration must be constant over the interval. When acceleration changes, describe the motion qualitatively and with sketched graphs instead of these equations.

   Review: 1.3 Representing Motion

8. Topic 1.4 · Work it outA train moves east at 20 m/s. A passenger walks at 2 m/s relative to the train. What is her velocity relative to the ground walking toward the front, then toward the back?

   Add velocities with signs, east positive. Toward the front: $20+2=22$ m/s east. Toward the back: $20-2=18$ m/s east.

   Review: 1.4 Reference Frames and Relative Motion

9. Topic 1.4 · Which one fitsA ball is dropped inside a train moving at constant velocity. Do a rider and a person on the platform measure the same velocity for the ball? The same acceleration?

   Different velocities, because the observed velocity combines the ball's motion with the motion of the observer's frame. The same acceleration, because acceleration is the same in all inertial reference frames.

   Review: 1.4 Reference Frames and Relative Motion

10. Topic 1.5 · Work it outA ball rolls off a 20 m high cliff at 8 m/s horizontally. How long is it in the air, and how far from the base does it land?

    Vertical: $20=\frac{1}{2}(10)t^2$, so $t=2$ s. Horizontal velocity stays constant: $(8)(2)=16$ m from the base.

    Review: 1.5 Vectors and Motion in Two Dimensions

11. Topic 1.5 · Spot the mistake"At the top of its path, a projectile's acceleration is zero." What is wrong?

    Only the vertical velocity is zero there. The acceleration is $10{\text{m/s}}^2$ downward for the whole flight, and the horizontal velocity has not changed.

    Review: 1.5 Vectors and Motion in Two Dimensions

Unit 2: Force and Translational Dynamics

1. Topic 2.1 · Work it outA 2 kg mass sits at $x=0$ and a 3 kg mass at $x=5$ m. Where is the center of mass?

   $x_{cm}=\frac{(2)(0)+(3)(5)}{2+3}=\frac{15}{5}=3$ m, closer to the heavier mass.

   Review: 2.1 Systems and Center of Mass

2. Topic 2.1 · Check the conditionsWhen can you treat a whole system, like a car full of passengers, as a single object?

   When the properties and interactions of its parts do not matter for the behavior you are modeling. Then the system acts like one object located at its center of mass.

   Review: 2.1 Systems and Center of Mass

3. Topic 2.2 · Spot the mistakeA student draws a free-body diagram of a ball after it leaves the thrower's hand and includes an upward "force of the throw." What is wrong?

   Every force comes from an interaction with another object. After release the hand is no longer touching the ball, so with air resistance ignored the only force is gravity from Earth, pointing down.

   Review: 2.2 Forces and Free-Body Diagrams

4. Topic 2.2 · Which one fitsA block slides down a ramp. Why tilt your coordinate axes so one axis runs along the ramp?

   The acceleration is along the ramp. With one axis parallel to the acceleration, the perpendicular direction has zero acceleration, which makes turning the free-body diagram into equations much simpler.

   Review: 2.2 Forces and Free-Body Diagrams

5. Topic 2.3 · Spot the mistakeA truck hits a small car head-on. "The truck pushes harder on the car than the car pushes on the truck." True?

   False. By Newton's third law the two forces are equal in magnitude and opposite in direction. The car has the larger acceleration because its mass is smaller.

   Review: 2.3 Newton’s Third Law

6. Topic 2.3 · Check the conditionsWhen is the tension the same everywhere in a rope?

   When the rope is ideal (negligible mass, no stretching) and any pulley it passes over is ideal too; a pulley with rotational inertia makes the tension differ on its two sides. In a rope or chain with mass, tension varies; a hanging chain has more tension near the top, since that part supports more of the chain.

   Review: 2.3 Newton’s Third Law

7. Topic 2.3 · Which one fitsTwo blocks are joined by a string and pulled across a table. If you choose both blocks as the system, does the string tension appear in $F_{net}$?

   No. The tension is an internal force between parts of the system, and internal forces do not change the motion of the system's center of mass. Only external forces go into $F_{net}$.

   Review: 2.3 Newton’s Third Law

8. Topic 2.4 · Spot the mistakeA puck slides across frictionless ice at a constant 5 m/s. "There must be a forward force keeping it moving." True?

   False. Constant velocity means zero net force. By Newton's first law the puck keeps its velocity with nothing pushing it forward.

   Review: 2.4 Newton’s First Law

9. Topic 2.4 · Know the termWhat is an inertial reference frame?

   A frame from which an observer would verify Newton's first law: an object with zero net force keeps a constant velocity. Assume problem frames are inertial unless told otherwise.

   Review: 2.4 Newton’s First Law

10. Topic 2.5 · Work it outA 3 kg block and a 2 kg block hang on either side of an ideal pulley. Find the acceleration of the blocks.

    Treat both blocks as one system. Net external force: $30-20=10$ N toward the 3 kg side. $a=\frac{10}{3+2}=2{\text{m/s}}^2$.

    Review: 2.5 Newton’s Second Law

11. Topic 2.6 · Work it outIf the distance between two planets' centers doubles, what happens to the gravitational force between them?

    It becomes one fourth as large, because $F_g=G\frac{m_1{m}_2}{r^2}$ and doubling $r$ multiplies $r^2$ by 4.

    Review: 2.6 Gravitational Force

12. Topic 2.6 · Work it outA 50 kg student stands on a scale in an elevator accelerating upward at $2{\text{m/s}}^2$. What does the scale read?

    The scale reads the normal force, which is the apparent weight. $F_n-mg=ma$, so $F_n=(50)(10+2)=600$ N, more than the 500 N gravitational force.

    Review: 2.6 Gravitational Force

13. Topic 2.6 · Spot the mistake"Astronauts on the space station float because there is no gravity up there." What is wrong?

    Earth's gravitational field at that height is still about 90 percent as strong as at the surface. They appear weightless because gravity is the only force on them, so there is no normal force and nothing to read as apparent weight.

    Review: 2.6 Gravitational Force

14. Topic 2.6 · Know the termWhat is the difference between inertial mass and gravitational mass?

    Inertial mass sets how much an object resists changes in its motion. Gravitational mass sets how strongly it is attracted to other masses. Experiments show the two are equivalent.

    Review: 2.6 Gravitational Force

15. Topic 2.7 · Work it outA 10 kg crate rests on a floor with ${\mu }_s=0.5$. You push horizontally with 20 N and it does not move. What is the static friction force?

    20 N, opposite your push. Static friction takes whatever value prevents slipping, up to a maximum of ${\mu }_s{F}_n=(0.5)(100)=50$ N.

    Review: 2.7 Kinetic and Static Friction

16. Topic 2.7 · Spot the mistake"Turning a brick onto its wide face increases the friction because more surface is touching." True?

    False. The friction force between two surfaces does not depend on the contact area. It depends on the normal force and the coefficient of friction for the materials.

    Review: 2.7 Kinetic and Static Friction

17. Topic 2.8 · Work it outAn ideal spring with $k=200$ N/m is stretched 0.05 m from its relaxed length. What force does it exert on the attached block?

    $|F_s|=k|\mathrm{\Delta }x|=(200)(0.05)=10$ N, directed back toward the equilibrium position.

    Review: 2.8 Spring Forces

18. Topic 2.8 · Say it in contextA graph shows spring force magnitude against stretch as a straight line through the origin. What does the slope mean?

    The slope is the spring constant $k$, in N/m. The straight line through the origin shows the force is proportional to the stretch, as Hooke's law says.

    Review: 2.8 Spring Forces

19. Topic 2.9 · Spot the mistakeA student adds an outward "centrifugal force" to the free-body diagram of a car rounding a flat curve. What is wrong?

    No object exerts that force. The net force on the car points toward the center of the circle, and here it comes from static friction from the road.

    Review: 2.9 Circular Motion

20. Topic 2.9 · Work it outA 1000 kg car rounds a flat curve of radius 50 m at 10 m/s. Find its centripetal acceleration and the net force needed.

    $a_c=\frac{v^2}{r}=\frac{100}{50}=2{\text{m/s}}^2$ toward the center. Net force: $(1000)(2)=2000$ N, supplied by static friction.

    Review: 2.9 Circular Motion

21. Topic 2.9 · Which one fitsA car rounds a banked curve with no friction needed. What force provides the centripetal acceleration?

    The horizontal component of the normal force from the road points toward the center of the curve. The vertical component balances gravity.

    Review: 2.9 Circular Motion

Unit 3: Work, Energy, and Power

1. Topic 3.1 · Work it outA 2 kg cart moves at 3 m/s. Find its kinetic energy, then find it again if the speed doubles.

   $K=\frac{1}{2}(2)(3{)}^2=9$ J. At 6 m/s, $K=\frac{1}{2}(2)(6{)}^2=36$ J: doubling the speed quadruples the kinetic energy.

   Review: 3.1 Translational Kinetic Energy

2. Topic 3.1 · Say it in contextA bag sits on a seat of a moving bus. A rider says its kinetic energy is zero; someone on the sidewalk says it is not. Who is right?

   Both. Kinetic energy depends on the observer's reference frame. In the bus frame the bag is at rest; in the sidewalk frame it moves with the bus.

   Review: 3.1 Translational Kinetic Energy

3. Topic 3.2 · Work it outYou pull a sled 4 m with a 50 N force at ${60}^{\circ }$ above the horizontal. How much work does your force do?

   $W=Fd\cos \theta =(50)(4)\cos {60}^{\circ }=(50)(4)(0.5)=100$ J. Only the component parallel to the displacement does work.

   Review: 3.2 Work

4. Topic 3.2 · Spot the mistake"The string does work on a ball whirled in a horizontal circle at constant speed." True?

   False. The string's force is perpendicular to the ball's displacement at every instant, so it does zero work. It changes the direction of motion without changing the kinetic energy.

   Review: 3.2 Work

5. Topic 3.2 · Say it in contextWhat does the area under a graph of the parallel force component versus displacement represent?

   The work done by that force over the interval. Area below the axis is negative work, meaning energy is transferred out of the system.

   Review: 3.2 Work

6. Topic 3.2 · Which one fitsA box is moved from A to B along a short path and along a long winding path. For which force is the work the same both ways: gravity or kinetic friction?

   Gravity. It is conservative, so its work depends only on the start and end positions. Friction is nonconservative: its work grows with the length of the path.

   Review: 3.2 Work

7. Topic 3.3 · Work it outA 2 kg book is lifted 3 m. By how much does the gravitational potential energy of the book-Earth system change?

   $\mathrm{\Delta }{U}_g=mg\mathrm{\Delta }y=(2)(10)(3)=60$ J, an increase.

   Review: 3.3 Potential Energy

8. Topic 3.3 · Spot the mistake"The ball has 40 J of gravitational potential energy." What does that statement leave out?

   Potential energy belongs to a system of interacting objects, here the ball and Earth, not to the ball alone. Its value also depends on where the observer chose to put zero.

   Review: 3.3 Potential Energy

9. Topic 3.4 · Know the termWhat is the mechanical energy of a system?

   The sum of the system's kinetic energy and potential energy. Friction and other nonconservative forces can turn some of it into thermal energy or sound.

   Review: 3.4 Conservation of Energy

10. Topic 3.4 · Check the conditionsWhen is the total mechanical energy of a system constant?

    When no external work is done on the system and there are no nonconservative interactions, such as friction, inside it. Otherwise energy is transferred in or out, or converted to thermal energy or sound.

    Review: 3.4 Conservation of Energy

11. Topic 3.4 · Work it outA 2 kg block slides at 4 m/s onto a rough floor where the friction force is 4 N. How far does it slide before stopping?

    Initial kinetic energy: $\frac{1}{2}(2)(4{)}^2=16$ J. Friction removes $fd$, so $d=\frac{16}{4}=4$ m. That energy becomes thermal energy.

    Review: 3.4 Conservation of Energy

12. Topic 3.5 · Work it outA motor lifts a 50 kg crate 4 m at constant speed in 10 s. What is its average power?

    Work against gravity: $mg\mathrm{\Delta }y=(50)(10)(4)=2000$ J. Average power: $\frac{2000}{10}=200$ W.

    Review: 3.5 Power

Unit 4: Linear Momentum

1. Topic 4.1 · Work it outRight is positive. A 0.5 kg ball moves left at 4 m/s. What is its momentum?

   $p=mv=(0.5)(-4)=-2$ kg m/s. Momentum is a vector in the same direction as the velocity, so it points left.

   Review: 4.1 Linear Momentum

2. Topic 4.1 · Know the termWhat makes an interaction a "collision" in the physics sense?

   The forces between the objects are much larger than the net external force during the brief interaction. That lets you compare momentum just before and just after while ignoring outside forces.

   Review: 4.1 Linear Momentum

3. Topic 4.2 · Work it outA 0.2 kg ball hits a wall at 10 m/s and bounces straight back at 10 m/s. Contact lasts 0.02 s. Find the change in momentum and the average force.

   Toward the wall positive: $\mathrm{\Delta }p=(0.2)(-10)-(0.2)(10)=-4$ kg m/s. $F_{avg}=\frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}=\frac{-4}{0.02}=-200$ N, so 200 N away from the wall.

   Review: 4.2 Change in Momentum and Impulse

4. Topic 4.2 · Say it in contextOn a net external force versus time graph, what is the area under the curve? On a momentum versus time graph, what is the slope?

   The area under the force-time graph is the impulse, which equals the change in momentum. The slope of the momentum-time graph is the net external force.

   Review: 4.2 Change in Momentum and Impulse

5. Topic 4.3 · Work it outA 2 kg cart at 3 m/s hits a stationary 1 kg cart and they stick. How fast do they move together?

   Momentum of the two-cart system is conserved: $(2)(3)=(2+1)v$, so $v=2$ m/s in the original direction.

   Review: 4.3 Conservation of Linear Momentum

6. Topic 4.3 · Check the conditionsWhen is the total momentum of a system constant?

   When the net external force on the system is zero. Choose the system to include every object involved in the interaction so that the forces between them are internal.

   Review: 4.3 Conservation of Linear Momentum

7. Topic 4.4 · Work it outIn the collision where a 2 kg cart at 3 m/s sticks to a 1 kg cart and both move at 2 m/s, how much kinetic energy is lost?

   Before: $\frac{1}{2}(2)(3{)}^2=9$ J. After: $\frac{1}{2}(3)(2{)}^2=6$ J. 3 J went to other forms of energy, so the collision is inelastic. Because the carts stick together, it is perfectly inelastic.

   Review: 4.4 Elastic and Inelastic Collisions

8. Topic 4.4 · Spot the mistake"In an elastic collision, each object leaves with the same kinetic energy it came in with." True?

   False. Only the system's total kinetic energy is the same before and after. Energy can move from one object to the other, as when a moving cart stops and the cart it hits takes off.

   Review: 4.4 Elastic and Inelastic Collisions

9. Topic 4.4 · Spot the mistake"Momentum is lost in an inelastic collision." What is wrong?

   With no net external force, momentum is conserved in every collision. What decreases in an inelastic collision is the system's kinetic energy.

   Review: 4.4 Elastic and Inelastic Collisions

Unit 5: Torque and Rotational Dynamics

1. Topic 5.1 · Work it outA wheel starts from rest with a constant angular acceleration of $2{\text{rad/s}}^2$. Find its angular velocity and angular displacement after 3 s.

   $\omega ={\omega }_0+\alpha t=0+(2)(3)=6$ rad/s. $\mathrm{\Delta }\theta =\frac{1}{2}\alpha t^2=\frac{1}{2}(2)(3{)}^2=9$ rad.

   Review: 5.1 Rotational Kinematics

2. Topic 5.1 · Say it in contextOn a graph of angular velocity versus time, what do the slope and the area under the curve represent?

   The slope is the angular acceleration. The area under the curve is the angular displacement. They work just like the slope and area on a linear velocity-time graph.

   Review: 5.1 Rotational Kinematics

3. Topic 5.2 · Spot the mistake"A point on the rim of a spinning disk has a larger angular velocity than a point near the center." True?

   False. All points on a rigid system share the same angular velocity. The rim point has the larger linear speed, because $v=r\omega$ and its $r$ is larger.

   Review: 5.2 Connecting Linear and Rotational Motion

4. Topic 5.3 · Work it outA 20 N force is applied 0.3 m from a bolt, perpendicular to the wrench. Find the torque, then find it if the force is at ${30}^{\circ }$ to the wrench.

   Perpendicular: $\tau =rF=(0.3)(20)=6$ N m. At ${30}^{\circ }$: $\tau =rF\sin \theta =(0.3)(20)(0.5)=3$ N m.

   Review: 5.3 Torque

5. Topic 5.3 · Spot the mistake"Pushing hard on a door at its hinges will swing it open." Why not?

   A force whose line of action passes through the axis has zero lever arm, so it exerts zero torque however large it is. Push far from the hinges and perpendicular to the door.

   Review: 5.3 Torque

6. Topic 5.4 · Say it in contextA hoop and a solid disk have the same mass and radius. Which has more rotational inertia about its center, and why?

   The hoop. All of its mass sits at the full radius, while much of the disk's mass is close to the axis. Mass farther from the axis adds more rotational inertia.

   Review: 5.4 Rotational Inertia

7. Topic 5.4 · Work it outTwo 2 kg balls sit at each end of a light rod, each 0.5 m from the axis at the rod's center. Find the rotational inertia.

   $I=\sum m_i{r}_i^2=(2)(0.5{)}^2+(2)(0.5{)}^2=1$ kg m^2.

   Review: 5.4 Rotational Inertia

8. Topic 5.4 · Which one fitsA rod can spin about its center or about one end. Which axis gives the larger rotational inertia?

   The end. Rotational inertia is smallest about an axis through the center of mass, and $I^{\prime }=I_{cm}+M{d}^2$ adds to it for any parallel axis a distance $d$ away.

   Review: 5.4 Rotational Inertia

9. Topic 5.5 · Work it outA 30 kg child sits 2 m left of a seesaw's pivot. Where must a 40 kg child sit for the seesaw to balance?

   Net torque zero: $(300)(2)=(400)d$, so $d=1.5$ m to the right of the pivot. The heavier child sits closer.

   Review: 5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form

10. Topic 5.5 · Check the conditionsA ball falls without spinning. Is it in rotational equilibrium, translational equilibrium, both, or neither?

    Rotational only. Gravity acts at the center of mass, so the net torque about it is zero and the angular velocity stays constant. The net force is not zero, so it is not in translational equilibrium.

    Review: 5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form

11. Topic 5.6 · Work it outA net torque of 6 N m acts on a wheel with rotational inertia 2 kg m^2. Find the angular acceleration.

    $\alpha =\frac{{\tau }_{net}}{I}=\frac{6}{2}=3{\text{rad/s}}^2$, in the same rotational direction as the net torque.

    Review: 5.6 Newton’s Second Law in Rotational Form

12. Topic 5.6 · Which one fitsA block hangs from a string wrapped around a pulley that has rotational inertia. What analyses do you need to find the block's acceleration?

    Two: Newton's second law for the block's linear motion and the rotational form, ${\tau }_{net}=I\alpha$, for the pulley, linked by $a=r\alpha$. The tension is less than the block's weight.

    Review: 5.6 Newton’s Second Law in Rotational Form

Unit 6: Energy and Momentum of Rotating Systems

1. Topic 6.1 · Work it outA wheel with rotational inertia 2 kg m^2 spins at 3 rad/s. Find its rotational kinetic energy.

   $K=\frac{1}{2}I{\omega }^2=\frac{1}{2}(2)(3{)}^2=9$ J.

   Review: 6.1 Rotational Kinetic Energy

2. Topic 6.1 · Spot the mistake"A fan spinning in place has no kinetic energy because its center of mass is not moving." True?

   False. The points on the spinning blades have linear speed, so the fan has rotational kinetic energy even though its center of mass is at rest.

   Review: 6.1 Rotational Kinetic Energy

3. Topic 6.2 · Work it outA constant torque of 5 N m turns a wheel through 4 rad. How much work does the torque do?

   $W=\tau \mathrm{\Delta }\theta =(5)(4)=20$ J, transferred into the wheel's rotational kinetic energy if nothing else acts.

   Review: 6.2 Torque and Work

4. Topic 6.2 · Say it in contextWhat does the area under a graph of torque versus angular position represent?

   The work done by that torque on the rigid system as it rotates through that angle.

   Review: 6.2 Torque and Work

5. Topic 6.3 · Work it outA 2 kg ball moves in a straight line at 3 m/s. Its path passes 4 m from point P at closest approach. What is its angular momentum about P?

   $L=rmv\sin \theta$, and $r\sin \theta$ is the 4 m perpendicular distance. $L=(4)(2)(3)=24$ kg m^2/s. An object moving in a straight line can have angular momentum.

   Review: 6.3 Angular Momentum and Angular Impulse

6. Topic 6.4 · Say it in contextA spinning skater pulls her arms in and spins faster. Explain using angular momentum.

   The ice exerts negligible external torque, so her angular momentum $L=I\omega$ stays constant. Pulling mass closer to the axis lowers $I$, so $\omega$ must increase.

   Review: 6.4 Conservation of Angular Momentum

7. Topic 6.4 · Check the conditionsWhen is the total angular momentum of a system constant?

   When the net external torque on the system is zero. A nonzero net external torque transfers angular momentum between the system and its surroundings.

   Review: 6.4 Conservation of Angular Momentum

8. Topic 6.5 · Which one fitsA hoop and a solid disk of equal mass and radius roll without slipping from rest down the same ramp. Which reaches the bottom first?

   The disk. Both convert the same potential energy, but the hoop has more rotational inertia, so more of its energy goes into rotation and less into translation. Its center moves slower.

   Review: 6.5 Rolling

9. Topic 6.5 · Spot the mistake"Friction always drains energy from a rolling ball." When is that wrong?

   In ideal rolling without slipping, the contact point does not slide, so static friction dissipates no energy. Only when the object slips does kinetic friction remove mechanical energy.

   Review: 6.5 Rolling

10. Topic 6.6 · Which one fitsFor a satellite and planet, which quantities stay constant in a circular orbit, and which change in an elliptical one?

    Circular: total mechanical energy, potential energy, the satellite's kinetic energy and its angular momentum are all constant. Elliptical: total mechanical energy and angular momentum stay constant, while potential and kinetic energy trade back and forth.

    Review: 6.6 Motion of Orbiting Satellites

11. Topic 6.6 · Know the termWhat is escape velocity?

    The speed at which the satellite-planet system's total mechanical energy is zero. With only gravity acting, a satellite at that speed moves away and its speed approaches zero at an infinite distance.

    Review: 6.6 Motion of Orbiting Satellites

Unit 7: Oscillations

1. Topic 7.1 · Check the conditionsWhat must be true of the restoring force for motion to be simple harmonic motion, and when does a pendulum qualify?

   The restoring force must be proportional to the displacement from equilibrium and opposite to it. A pendulum qualifies only for small angular displacements, where the restoring torque is proportional to the angle.

   Review: 7.1 Defining Simple Harmonic Motion (SHM)

2. Topic 7.1 · Spot the mistake"At the equilibrium position the oscillating block is at rest." What is wrong?

   Equilibrium means the net force is zero there, not that the block is still. In SHM the block moves fastest as it passes through equilibrium.

   Review: 7.1 Defining Simple Harmonic Motion (SHM)

3. Topic 7.1 · Know the termDefine a restoring force and an equilibrium position.

   An equilibrium position is where the net force on the object is zero. A restoring force points opposite the object's displacement from that position, back toward it.

   Review: 7.1 Defining Simple Harmonic Motion (SHM)

4. Topic 7.2 · Work it outA 2 kg block on an ideal spring with $k=200$ N/m oscillates. Find the period.

   $T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{0.01}=0.2\pi \approx 0.63$ s.

   Review: 7.2 Frequency and Period of SHM

5. Topic 7.2 · Spot the mistake"Doubling the mass of a pendulum bob makes it swing more slowly." True?

   False. A simple pendulum's period depends on its length and $g$, not its mass. Doubling the mass of a block on a spring, though, does increase that period.

   Review: 7.2 Frequency and Period of SHM

6. Topic 7.3 · Say it in contextA block on a spring oscillates. At the turning points and at equilibrium, where are velocity and acceleration zero, and where are they largest?

   At the turning points, velocity is zero and acceleration has its largest magnitude. At equilibrium, velocity has its largest magnitude and acceleration is zero.

   Review: 7.3 Representing and Analyzing SHM

7. Topic 7.3 · Work it outA block's position is $x=0.1\cos (4\pi t)$, with $x$ in meters and $t$ in seconds. Find the amplitude, frequency and period.

   Match to $x=A\cos (2\pi ft)$: amplitude 0.1 m, $2\pi f=4\pi$ so $f=2$ Hz, and $T=\frac{1}{f}=0.5$ s.

   Review: 7.3 Representing and Analyzing SHM

8. Topic 7.4 · Work it outA spring with $k=100$ N/m oscillates with amplitude 0.2 m. Find the total energy and the maximum kinetic energy.

   $E=\frac{1}{2}k{A}^2=\frac{1}{2}(100)(0.2{)}^2=2$ J. The maximum kinetic energy is also 2 J, reached at equilibrium where potential energy is zero.

   Review: 7.4 Energy of Simple Harmonic Oscillators

9. Topic 7.4 · Say it in contextThe amplitude of a spring-block oscillator is doubled. What happens to its total energy and its period?

   Total energy is multiplied by 4, since $E=\frac{1}{2}k{A}^2$. The period does not change.

   Review: 7.4 Energy of Simple Harmonic Oscillators

Unit 8: Fluids

1. Topic 8.1 · Work it outA 2 kg sample of liquid has a volume of 0.002 m^3. Find its density.

   $\rho =\frac{m}{V}=\frac{2}{0.002}=1000$ kg/m^3, the density of water.

   Review: 8.1 Internal Structure and Density

2. Topic 8.1 · Know the termWhat two properties make a fluid "ideal" in AP Physics 1?

   It is incompressible, so its density stays constant, and it has no viscosity. Unless a problem says otherwise, every fluid is treated as ideal.

   Review: 8.1 Internal Structure and Density

3. Topic 8.2 · Work it outFind the gauge pressure 5 m below the surface of water ($\rho =1000$ kg/m^3). Then find the absolute pressure, taking $P_{atm}=1.0\times {10}^5$ Pa.

   $P_{gauge}=\rho gh=(1000)(10)(5)=5.0\times {10}^4$ Pa. Absolute: $1.0\times {10}^5+5.0\times {10}^4=1.5\times {10}^5$ Pa.

   Review: 8.2 Pressure

4. Topic 8.2 · Spot the mistake"Water pressure at the bottom of a pool points downward." What is wrong?

   Pressure is a scalar with no direction. The force it produces on any surface is perpendicular to that surface, so water pushes sideways on the walls and upward on a submerged object's bottom.

   Review: 8.2 Pressure

5. Topic 8.3 · Work it outA block of volume 0.002 m^3 is held fully under water ($\rho =1000$ kg/m^3). Find the buoyant force.

   $F_b=\rho Vg=(1000)(0.002)(10)=20$ N, equal to the weight of the water the block displaces.

   Review: 8.3 Fluids and Newton’s Laws

6. Topic 8.3 · Spot the mistake"A steel ball sinks, so the water exerts no buoyant force on it." What is wrong?

   The water still pushes up with a force equal to the weight of the water displaced. The ball sinks because its weight is larger than that buoyant force.

   Review: 8.3 Fluids and Newton’s Laws

7. Topic 8.3 · Know the termWhat is the buoyant force, and what exerts it?

   The net upward force a fluid exerts on an object in it. It is the combined result of the forces from all the fluid particles pushing on the object's surface.

   Review: 8.3 Fluids and Newton’s Laws

8. Topic 8.4 · Work it outWater flows at 2 m/s through a pipe of cross-sectional area 0.04 m^2, which narrows to 0.01 m^2. How fast does it flow in the narrow part?

   Continuity: $A_1{v}_1=A_2{v}_2$, so $(0.04)(2)=(0.01)v_2$ and $v_2=8$ m/s.

   Review: 8.4 Fluids and Conservation Laws

9. Topic 8.4 · Say it in contextIn a horizontal pipe, water speeds up where the pipe narrows. What does Bernoulli's equation say about the pressure there?

   It is lower. With no height change, $P+\frac{1}{2}\rho v^2$ stays constant along the flow, so a larger speed comes with a smaller pressure.

   Review: 8.4 Fluids and Conservation Laws