Conservation of Angular Momentum AP Physics C Mechanics MCQ – Exam Style Questions etc.
Conservation of Angular Momentum AP Physics C Mechanics MCQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Question
A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs?
(A) Linear momentum is converted to angular momentum.
(B) Kinetic energy is converted to angular momentum.
(C) Rotational kinetic energy is conserved.
(D) Translational kinetic energy is conserved.
(E) Linear momentum and angular momentum are both conserved.
Answer/Explanation
Ans:E
Question
What is the fewest number of the following conditions to ensure that angular momentum is conserved?
I. Conservation of linear momentum
II. Zero net external force
III. Zero net external torque
(A) II only
(B) III only
( C) I and II only
(D) I and III only
(E) II and III only
Answer/Explanation
Ans: B
Angular momentum is conserved when no net external torque is applied, which is (III). However, a body can experience a net nonzero torque even when the net external force is zero ( which is the condition that guarantees conservation of linear momentum), so neither (I) nor (II) necessarily ensure conservation of angular momentum.
Question
A bullet is moving with a velocity \(v_0\) when it collides with and becomes embedded in a wooden bar that is hinged at one end, as shown above. Consider the bullet and the wooden bar to be the system. For this scenario, which of the following is true?
(A) The linear momentum of the system is conserved because the net force on the system is zero.
(B) The angular momentum of the system is conserved because the net torque on the system is zero.
(C) The kinetic energy of the system is conserved because it is an inelastic collision.
(D) The kinetic energy of the system is conserved because it is an elastic collision.
(E) Linear momentum and angular momentum are both conserved.
Answer/Explanation
Ans: B
When objects stick together, a perfectly inelastic collision has occurred. For this situation, kinetic energy is not conserved. This eliminates (C) and (D) . Linear momentum is conserved when the net force on the system is zero. In this situation the hinge in the bar is exerting a force on it prohibiting it from translating to the right. Therefore linear momentum is not conserved. This eliminates (A) and (E). Angular momentum is conserved when the net torque on a system is zero. The force exerted by the hinge provides no torque because the lever arm is zero. Therefore, (B) is correct.
Questions (a) and (b)
A rigid rod of length L and mass M is floating at rest in space far from a gravitational field. A small blob of putty of mass m < M is moving to the right, as shown above. The putty hits and sticks to the rod a distance 2L/3 from the top end.
Question(a)
How will the rod/putty contraption move after the collision?
(A) The contraption will have no translational motion, but will rotate about the rod’s center of mass.
(B) The contraption will have no translational motion, but will rotate about the center of mass of the rod and putty combined.
(C) The contraption will move to the right and rotate about the position of the putty.
(D) The contraption will move to the right and rotate about the center of mass of the rod and putty combined.
(E) The contraption will move to the right and rotate about the rod’s center of mass.
Answer/Explanation
Ans:
D—By conservation of linear momentum, there is momentum to the right before collision, so there must be momentum to the right after collision as well. A free-floating object rotates about its center of mass; because the putty is attached to the rod, the combination will rotate about its combined center of mass.