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 · Decide and justify
A ceiling fan turns at a steady rate. Its center of mass, at the middle of the fan, stays at rest the whole time. A student says the turning fan has no kinetic energy, because its center of mass is not moving. Is the student right?
Which reason supports your answer?
Question 2 · from 6.2 · Calculate
A mechanic tightens a lug nut with a wrench. She exerts a steady torque of 35 N·m on the nut, in the sense the nut turns, while it turns through 150°. How much work does her torque do on the nut? Give your answer to the nearest 1 J.
Question 3 · from 6.3 · Sketch the graph
A wheel turns on a frictionless axle, with counterclockwise as positive. At 0 s its angular momentum is +1.0 kg·m²/s. A graph of the net torque on the wheel against time reads +0.50 N·m from 0 to 2 s, 0 from 2 s to 3 s, and -1.0 N·m from 3 s to 6 s. Sketch the wheel's angular momentum against time from 0 to 6 s. The first point is fixed at the wheel's angular momentum at 0 s.
One shape that fits
Drag a point up or down, or tap it and use the arrow keys. The shape is checked, and the graph must pass through the values the question gives.
Setup for question 4
A student tests a model clutch. Disk A, a heavy steel disk with a rotational inertia of 0.40 kg·m² about a vertical axle, spins counterclockwise, seen from above, which she takes as positive. At 0 s she drops disk B, which is not turning, from just above disk A onto it, centered on the same axle. The disks slip against each other until they turn together. Friction at the axle and air resistance are negligible. A rotary sensor on each disk records its angular velocity.
| Time (s) | Disk A (rad/s) | Disk B (rad/s) |
|---|---|---|
| 0 | 10.0 | 0.0 |
| 0.1 | 8.5 | 1.0 |
| 0.2 | 7.0 | 2.0 |
| 0.3 | 5.5 | 3.0 |
| 0.4 | 4.0 | 4.0 |
| 0.5 | 4.0 | 4.0 |
Question 4 · from 6.4 · Calculate
Using the clutch table, with counterclockwise as positive, what is the rotational inertia of disk B about the axle? Give your answer to the nearest 0.01 kg·m².
Setup for question 5
A new situation, and the reverse of the bowling ball: here the ball starts with spin and no forward motion. You spin a basketball so that, seen from the side, it turns clockwise with its center not moving, then set it gently on a level gym floor. At first it skids. Before you answer, picture which way the bottom of a clockwise ball moves, and which way friction on the ball must then point.
Question 5 · from 6.5 · Draw the forces
Seen from the side, a 0.60 kg basketball spins clockwise with its center at rest, and you set it on a level gym floor. Just after it touches down, its bottom skids to the left over the floor, and the coefficient of kinetic friction between ball and floor is 0.50. Build the free-body diagram of the ball while it skids, and set each arrow's length to compare the forces.
The dot is the basketball. One diagram that fits
Pick each force exerted on the basketball, then choose the way it points and how long its arrow is compared with the others. The arrows are drawn for you.
Setup for question 6
A 1,000 kg satellite moves in an elliptical orbit around Earth, and only Earth's gravity acts on it. Point A is the closest point of its orbit and point C the farthest. The table gives the satellite's distance from Earth's center at three points, the gravitational potential energy of the satellite-Earth system there, with zero at infinite separation, and the satellite's kinetic energy. One kinetic energy has not been filled in. Energies are in gigajoules, where 1 GJ is J.
| Point | Distance from Earth's center (m) | Gravitational potential energy (GJ) | Kinetic energy (GJ) |
|---|---|---|---|
| A | -50.0 | 40.0 | |
| B | -25.0 | 15.0 | |
| C | -12.5 | ? |
Question 6 · from 6.6 · Calculate
Using the satellite table, what is the satellite's kinetic energy at point C? Give your answer in gigajoules, to the nearest 0.1 GJ.
Question 7 · from 6.1 · Sketch the graph
A lab flywheel has a rotational inertia of 0.50 kg·m² about its axle. Sketch its rotational kinetic energy against its angular speed, from 0 to 8.0 rad/s. The first point is fixed at 0.
One shape that fits
Drag a point up or down, or tap it and use the arrow keys. The shape is checked, and the graph must pass through the values the question gives.
Question 8 · from 6.2 · Sketch the graph
A motor starts a grinding wheel from rest. Its torque on the wheel is a steady 6.0 N·m while the wheel turns through its first 3.0 rad, then falls steadily to zero at 6.0 rad. Friction is negligible, so the motor's torque is the only one doing work on the wheel. Sketch the wheel's rotational kinetic energy against its angular position from 0 to 6.0 rad. The first point is fixed at 0.
One shape that fits
Drag a point up or down, or tap it and use the arrow keys. The shape is checked, and the graph must pass through the values the question gives.
Setup for question 9
A new situation: nothing here turns at all. A skater glides straight across a frozen pond past a lamp post at its edge, and the question is her angular momentum about the post.
Question 9 · from 6.3 · Calculate
A 60 kg skater glides in a straight line across level ice at a steady 3.0 m/s, and friction is negligible. At one instant she is 5.0 m from a lamp post, and the angle between the line from the post to her and her velocity is 150°. What is the magnitude of her angular momentum about the post?
Uses the same setup as question 4, above.
Question 10 · from 6.4 · Multiple choice
Using the clutch table, with counterclockwise as positive, which describes the angular impulse that disk B exerted on disk A from 0 s to 0.4 s?
0 of 10 answered.