Physics Practice Test: Torque and Rotational Motion
- Torque and Rotational Motion
- 10 questions
- 13 minutes
This test covers torque, balancing objects, moment of inertia and angular momentum. Use g = 9.8 m/s². Tip: only the part of the force perpendicular to the lever arm creates torque.
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Question 1
A mechanic pushes with a force of 40 N at the end of a wrench, 0.25 m from the bolt, perpendicular to the handle. What torque does she apply?
Correct answer: A
Torque = force × lever arm = 40 N × 0.25 m = 10 N·m when the force is perpendicular. Dividing 40 by 0.25 gives 160, which is the wrong operation.
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Question 2
A force of 50 N is applied 0.40 m from a pivot at an angle of 30° to the lever arm. What is the torque?
Correct answer: C
τ = rF sin θ = 0.40 × 50 × sin 30° = 0.40 × 50 × 0.5 = 10 N·m. Ignoring the angle gives 20 N·m, and using cos 30° gives about 17 N·m.
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Question 3
A 30 kg child sits 2.0 m from the pivot of a seesaw. How far from the pivot, on the other side, must a 40 kg child sit to balance it?
Correct answer: B
For balance the torques are equal: 30 × 2.0 = 40 × d, so d = 60 ÷ 40 = 1.5 m. The heavier child must sit closer; 2.7 m comes from flipping the ratio.
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Question 4
Why are door handles placed on the side opposite the hinges?
Correct answer: D
Torque equals force times distance from the axis, so pushing far from the hinges turns the door with less effort. Pushing near the hinges needs a much larger force for the same torque.
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Question 5
Which conditions must both be true for an object to be in static equilibrium?
Correct answer: D
With zero net force the object does not start moving, and with zero net torque it does not start rotating. A pair of equal, opposite forces along different lines can give zero net force but still spin an object.
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Question 6
A uniform 4.0 m plank of mass 20 kg rests on two supports, one at each end. A 60 kg painter stands 1.0 m from the left end. What upward force does the right support provide?
Correct answer: B
Taking torques about the left end: F × 4.0 = (20 × 9.8)(2.0) + (60 × 9.8)(1.0) = 392 + 588 = 980, so F = 245 N. The left support carries the rest, 784 − 245 = 539 N, because the painter is closer to it.
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Question 7
A wheel with a moment of inertia of 3.0 kg·m² is acted on by a net torque of 12 N·m. What is its angular acceleration?
Correct answer: A
From τ = Iα, α = τ ÷ I = 12 ÷ 3.0 = 4.0 rad/s². Multiplying instead of dividing gives 36 rad/s².
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Question 8
A solid disk and a thin ring have the same mass and radius. Both are released together and roll without slipping down the same ramp. Which reaches the bottom first?
Correct answer: B
The ring has all its mass at the rim, so it has a larger moment of inertia and more of its energy goes into spinning. The disk keeps more energy as forward motion and wins; their masses are equal anyway.
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Question 9
A figure skater spins at 2.0 rev/s with a moment of inertia of 4.0 kg·m². She pulls her arms in, and her moment of inertia drops to 1.6 kg·m². What is her new spin rate?
Correct answer: C
Angular momentum is conserved: 4.0 × 2.0 = 1.6 × ω, so ω = 8.0 ÷ 1.6 = 5.0 rev/s. Getting 0.80 rev/s means the ratio was flipped; a smaller moment of inertia must mean faster spinning.
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Question 10
A tall bookcase is tilted slowly on one edge. At what point will it fall over instead of settling back?
Correct answer: C
Once the center of gravity is past the pivot edge, the weight creates a torque that turns the bookcase further over. Before that point, the weight’s torque pulls it back, so tilting alone does not make it fall.
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