Torque and Rotational Motion Practice Questions
AP (Advanced Placement) · AP Physics 1 · 150 free MCQs with instant results and detailed explanations.
150
Total
50
Easy
72
Medium
28
Hard
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Sample Questions from Torque and Rotational Motion
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Q1
Easy
A student is trying to balance a seesaw that is 3.0 m long. If a 60 kg child sits 1.5 m from the fulcrum, how far must a 40 kg child sit from the fulcrum to achieve equilibrium?
A.
2.25 m
B.
1.5 m
C.
1.0 m
D.
3.0 m
Show Answer & Explanation
Correct Answer: A
To balance the seesaw, the moments must be equal. Thus, 60 kg ร 1.5 m = 40 kg ร d. Solving for d gives d = (60 kg ร 1.5 m) / 40 kg = 2.25 m.
Q2
Easy
What is the torque produced by a force of 10 N applied perpendicularly at a distance of 2 m from the pivot point?
A.
20 Nยทm
B.
10 Nยทm
C.
5 Nยทm
D.
0 Nยทm
Show Answer & Explanation
Correct Answer: A
Torque is calculated as the product of force and lever arm distance when the force is applied perpendicularly. Here, torque = 10 N * 2 m = 20 Nยทm.
Q3
Easy
If an object is in rotational equilibrium, which of the following statements must be true?
A.
The net torque acting on the object is zero.
B.
The object's angular speed is increasing.
C.
The object is not subjected to any forces.
D.
The object is moving in a straight line.
Show Answer & Explanation
Correct Answer: A
For an object to be in rotational equilibrium, the net torque acting on it must be zero. This means that all the torques are balanced, leading to no angular acceleration.
Q4
Medium
A uniform disk with a radius of 0.5 m and mass 4 kg is rotating about its center with an angular velocity of 2 rad/s. What is its rotational kinetic energy?
A.
4 J
B.
8 J
C.
16 J
D.
32 J
Show Answer & Explanation
Correct Answer: C
The rotational kinetic energy (K.E.) is given by K.E. = (1/2) I ฯยฒ. The moment of inertia (I) for a disk is (1/2) m rยฒ. Substituting m = 4 kg, r = 0.5 m, and ฯ = 2 rad/s, we find K.E. = (1/2) * (1/2 * 4 * 0.5ยฒ) * (2ยฒ) = 16 J.
Q5
Medium
If the net torque acting on a rotating object is zero, what can be concluded about its angular velocity?
A.
It must be zero.
B.
It is constant.
C.
It is increasing.
D.
It is decreasing.
Show Answer & Explanation
Correct Answer: B
According to the rotational analog of Newton's first law, if the net torque is zero, the angular momentum remains constant, which means the angular velocity will also be constant, not necessarily zero.
Q6
Medium
A flywheel rotates at 10 rad/s and accelerates uniformly to 20 rad/s in 5 seconds. What is the angular acceleration of the flywheel?
A.
2 rad/sยฒ
B.
1 rad/sยฒ
C.
0.5 rad/sยฒ
D.
3 rad/sยฒ
Show Answer & Explanation
Correct Answer: A
Angular acceleration (ฮฑ) is calculated using the formula ฮฑ = (ฯ_final - ฯ_initial) / t. Here, ฯ_final = 20 rad/s, ฯ_initial = 10 rad/s, and t = 5 s. Thus, ฮฑ = (20 - 10) / 5 = 2 rad/sยฒ.
Q7
Medium
A disk of radius R is rotating with an angular velocity ฯ. What is the linear velocity of a point on the edge of the disk?
A.
Rฯ
B.
ฯ/R
C.
R/ฯ
D.
Rยฒฯ
Show Answer & Explanation
Correct Answer: A
The linear velocity (v) of a point on the edge of a rotating disk is given by the formula v = Rฯ, where R is the radius and ฯ is the angular velocity. This relationship shows how linear velocity is directly proportional to both the radius and the angular velocity.
Q8
Hard
A solid disk of radius R and mass M is rotating about its central axis with an angular velocity ฯ. What is the magnitude of the torque required to bring the disk to rest in a time interval t?
A.
Iฯ/t
B.
MฯR/t
C.
0.5Iฯ/t
D.
2MฯR/t
Show Answer & Explanation
Correct Answer: A
The torque ฯ needed to change angular momentum is given by ฯ = Iฮฑ, where ฮฑ is the angular acceleration. The moment of inertia I of a disk is (1/2)MRยฒ. To bring the disk to rest, we have ฮฑ = -ฯ/t, so the torque is I(-ฯ/t) = (1/2)MRยฒ(-ฯ/t) = -Iฯ/t. The magnitude is Iฯ/t, confirming option A.
Q9
Hard
A beam is pivoted at one end and has a mass m1 at the free end. If a second mass m2 is placed at a distance d from the pivot on the beam, what is the condition for static equilibrium when the beam is horizontal?
A.
m1gR = m2gd
B.
m1gR = m2g(d + R)
C.
m1gR = m2g(d - R)
D.
m1gR + m2gd = 0
Show Answer & Explanation
Correct Answer: A
For the beam to be in static equilibrium, the clockwise torque must equal the counterclockwise torque. The torque due to m1 is m1gR and the torque due to m2 is m2gd. Setting these equal gives m1gR = m2gd, confirming that option A is correct.
Q10
Hard
A solid disk of mass 4 kg and radius 0.5 m is rotating about its central axis with an angular velocity of 10 rad/s. What is the rotational kinetic energy of the disk?
A.
100 J
B.
80 J
C.
50 J
D.
200 J
Show Answer & Explanation
Correct Answer: A
The rotational kinetic energy (KE_rot) is given by the formula KE_rot = (1/2) * I * ฯยฒ. For a solid disk, the moment of inertia (I) is (1/2) * m * rยฒ. Calculating it yields KE_rot = (1/2) * (1/2 * 4 kg * (0.5 m)ยฒ) * (10 rad/s)ยฒ = 100 J.
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Torque and Rotational Motion โ AP (Advanced Placement) AP Physics 1 Practice Questions Online
This page contains 150 practice MCQs for the chapter Torque and Rotational Motion in AP (Advanced Placement) AP Physics 1. The questions are organized by difficulty โ 50 easy, 72 medium, 28 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.