Unit 6 check

Unit 6 check: Energy and Momentum of Rotating Systems

10 questions from 6 lessons in Unit 6. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 6.1 · Calculate

A bench grinder's wheel has a rotational inertia of 0.040 kg·m² about its axle and turns at 50 revolutions per second. What is its rotational kinetic energy?

Your answer J

Question 2 · from 6.2 · Calculate

An electric motor exerts a constant torque of 0.40 N·m on a grinding wheel, counterclockwise as seen from the front, while the wheel turns 25 revolutions counterclockwise. Take counterclockwise as seen from the front as positive. How much work does the motor's torque do on the wheel?

Your answer J

Setup for question 3

On paper. Sketch the potter's wheel's angular momentum against time, from the worked example in Watch it done, from $t = 0$ to $t = 2.0$ s, with a label and a unit on each axis. Mark its starting value, and say where the graph is steepest and which quantity sets how steep it is. There is nothing to submit. Compare: $L$ starts at 2.4 kg·m²/s with zero slope and curves upward the whole time, steepest at 2.0 s, where its slope is the net torque then, 4.0 N·m. The graph at the top of the page has a different shape because its torque rises and then falls.

Question 3 · from 6.3 · Rank it

Three objects move about a vertical axis through point O, all counterclockwise as seen from above. Disk A, centered on the axis, has rotational inertia 0.50 kg·m² about it and spins at 8.0 rad/s. Ball B, of mass 2.0 kg, slides at a steady 3.0 m/s in a straight line that passes 0.50 m from O at its closest. Hoop C, centered on the axis, has rotational inertia 2.0 kg·m² about it and spins at 2.0 rad/s. Rank them by the size of their angular momentum about the axis.

Greatest first

Give each one a place, 1 for first. Give two the same place if they are equal.

Disk A
Ball B
Hoop C

Your ranking: none yet

Setup for question 4

On paper. You have a stool that turns on a low-friction bearing, two hand weights, a meterstick and a phone with a gyroscope app that can be taped to the stool. Write a procedure to test whether a rider's angular momentum stays constant as she pulls the weights in toward her chest: what you would measure in each arm position and with what, how you would find her rotational inertia in each position, and which outside torque you would try to keep small, and how. There is nothing to submit here; compare your plan with the stool readings in Check yourself.

Question 4 · from 6.4 · Rank it

Three identical platforms, each of radius 1.2 m with rotational inertia 4.0 kg·m², turn counterclockwise, as seen from above, at 6.0 rad/s on frictionless vertical axles. A sandbag is dropped straight down from rest onto each and stays where it lands: on platform A a 2.0 kg bag lands 0.50 m from the axle, on B a 4.0 kg bag lands 0.25 m from the axle, and on C a 1.0 kg bag lands 1.0 m from the axle. Treat each bag as a point. Rank the platforms by angular speed after the bags land.

Greatest first

Give each one a place, 1 for first. Give two the same place if they are equal.

Platform A
Platform B
Platform C

Your ranking: none yet

Setup for question 5

On paper. Draw a force diagram for a solid ball rolling without slipping down a ramp, with each force drawn where it is exerted and labeled with what exerts it. Then describe how you could find out, in your lab, whether a soup can rolls without slipping down a ramp, using a meterstick and a strip of tape on the can's rim: what you would measure, how many times, and what result would show the can slipping. There is nothing to submit here.

Question 5 · from 6.5 · Rank it

Four objects are released from rest at the top of the same ramp, one at a time, and each rolls without slipping to the bottom. A is a hoop ( $I_{cm} = M R^{2}$ ) of mass 2.0 kg and radius 0.10 m. B is a solid sphere ( $I_{cm} = \frac{2}{5} M R^{2}$ ) of mass 0.50 kg and radius 0.050 m. C is a solid disk ( $I_{cm} = \frac{1}{2} M R^{2}$ ) of mass 1.0 kg and radius 0.20 m. D is a solid sphere of mass 3.0 kg and radius 0.15 m. Ignore air resistance. Rank the objects by the speed of their centers at the bottom.

Fastest first

Give each one a place, 1 for first. Give two the same place if they are equal.

A, the hoop
B, the small sphere
C, the disk
D, the large sphere

Your ranking: none yet

Setup for question 6

A 200 kg probe moves in an elliptical orbit around the invented planet Tolla, of mass $3.0 \times 10^{24}$ kg and radius $2.5 \times 10^{6}$ m, with its engine off. Gravity from Tolla is the only force on it, and $U_{g}$ is zero at infinite separation. Use $G = 6.67 \times 10^{- 11}$ N·m²/kg². At the closest and farthest points, the probe's velocity is perpendicular to the line from Tolla's center to the probe. Tracking gives:

Tracking data for the probe
Point in the orbit	Distance from Tolla's center (m)	Speed (m/s)
Closest point	$3.2 \times 10^{6}$	$1.0 \times 10^{4}$
Farthest point	$1.28 \times 10^{7}$	not tracked

Question 6 · from 6.6 · Calculate

Using the tracking data, what is the probe's speed at its farthest point?

Your answer m/s

Question 7 · from 6.1 · Fill the statement

A baton is two small 0.50 kg balls on the ends of a light rod 0.80 m long. It spins at 6.0 rad/s about a fixed axis through the middle of the rod, perpendicular to it, so its center of mass stays at rest.

Each ball moves at . Adding the two balls' $\frac{1}{2} m v^{2}$ gives , and $\frac{1}{2} I ω^{2}$ with $I = \sum m_{i} r_{i}^{2}$ comes out .

Question 8 · from 6.2 · Rank it

Three motors each turn a shaft from $θ = 0$ to $θ = 2.0$ rad, counterclockwise as seen from the motor, which is the positive sense, and every torque is counterclockwise. Motor A's torque is a constant 3.0 N·m. Motor B's torque rises steadily from 0 at 0 rad to 5.0 N·m at 2.0 rad. Motor C's torque falls steadily from 7.0 N·m at 0 rad to 0 at 2.0 rad. Rank the motors by the work each torque does on its shaft.

Most work first

Give each one a place, 1 for first. Give two the same place if they are equal.

Motor A
Motor B
Motor C

Your ranking: none yet

Setup for question 9

Question 9 · from 6.3 · Calculate

A grinding wheel has a rotational inertia of 0.20 kg·m² about its axle and turns counterclockwise, as seen from the front, at 15 rad/s. Take counterclockwise as positive. Its reversible motor then exerts a constant net torque of 1.5 N·m clockwise for 3.0 s. What is the wheel's angular velocity at the end of the 3.0 s?

Your answer rad/s

Setup for question 10

Question 10 · from 6.4 · Calculate

A potter's wheel and the clay on it, together a rigid system with rotational inertia 0.80 kg·m², turn counterclockwise, as seen from above, at 12 rad/s. The motor is switched off, and the potter presses wet hands against the spinning clay, exerting a friction torque of 2.4 N·m in the clockwise sense for 1.5 s. Ignore friction in the bearing. Take counterclockwise as positive. What is the wheel's angular velocity at the end of the 1.5 s?

Your answer rad/s

0 of 10 answered.