Conservation of Angular Momentum AP Physics 1 MCQ – Exam Style Questions etc.
Conservation of Angular Momentum AP Physics 1 MCQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Exam Style Practice Questions, Conservation of Angular Momentum AP Physics 1 MCQ
Question
A disk of radius 1 m and rotational inertia I = 0.5 kg.m2 is free to rotate, but initially at rest. A blob of putty with mass 0.1 kg is traveling toward the disk with a speed of 10 m/s, as shown in the preceding figure. The putty collides with the outermost portion of the disk and sticks to the disk. What is the angular momentum of the combined disk-putty system after the collision?
(A) 5 \(kg\cdot m^{2}/s\)
(B) 1 \(kg\cdot m^{2}/s\)
(C) 0.5 \(kg\cdot m^{2}/s\)
(D)0 \(kg\cdot m^{2}/s\)
▶️Answer/Explanation
Ans:
B—In a collision, momentum—including angular momentum—is conserved. The question might as well be asking, “What is the angular momentum of the two objects before the collision?” And since the disk is at rest initially, the question is asking the even easier question, “What is the angular momentum of the putty before collision?” The axis of rotation is the center of the disk. The putty is a point mass; the angular momentum of a point mass is mvr with r the distance of closest approach to the axis. That’s (0.1 kg)(10 m/s)(1 m) = 1 \(kg\cdot m^{2}/s\).
Question
Three wagons each have the same total mass (including that of the wheels) and four wheels, but the wheels are differently styled. The structure, mass, and radius of each wagon’s wheels are shown in the preceding chart. In order to accelerate each wagon from rest to a speed of 10 m/s, which wagon requires the greatest energy input?
(A) Wagon A
(B) Wagon B
(C) Wagon C
(D) All require the same energy input
▶️Answer/Explanation
Ans:A
The energy input must be enough to change the translational kinetic energy of the cart and to change the rotational kinetic energy of the wheels. Since the wheels are all of the same radius, they will rotate with the same angular speed when the wagon reaches 10 m/s. Whichever wheels have the largest rotational inertia will therefore require the largest energy input to get to the same speed. Calculating, wagon A has the largest rotational inertia of 0.0025 \(kg\cdot m^{2}\).