Rolling AP Physics C Mechanics MCQ – Exam Style Questions etc.
Rolling AP Physics C Mechanics MCQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Question
a disk is free to rotate about an axis perpendicular to the disk through its center. If the disk starts from rest and accelerates uniformly at the rate of 3 radians/s2 for 4 s, its angular displacement during this time is
(A) 6 radians (B) 12 radians (C) 18 radians (D) 24 radians (E) 48 radians
Answer/Explanation
Ans:D
Solution: θ = ω0t + ½ αt2
Question
A uniform cylinder, initially at rest on a frictionless, horizontal surface, is pulled by a constant force F from time t = o to time t = T. From time t = Ton, this force is removed. Which of the following graphs best illustrates the speed, v, of the cylinder’s center of mass from t = o to t = 2T?
Answer/Explanation
Ans: B
The cylinder slides across the surface with acceleration a = F/m until time t = T, when a drops to zero (because F becomes zero). Therefore, from time t = o tot= T, the
velocity is steadily increasing (because the acceleration is a positive constant), but, at t = T, the velocity remains constant. This is illustrated in graph (B).
Question
The solid disk shown has mass M and radius R. The rotational inertia of the disk about axis 1, which passes through the disk’s center, is (1/2)\(MR^{2}\). What is the rotational inertia of the disk about axis 2, which is tangential to the disk’s edge?
(A) (3/2)\(MR^{2}\)
(B) (2/5)\(MR^{2}\)
(C) \(MR^{2}\)
(D) (1/3)\(MR^{2}\)
(E) (2/3)\(MR^{2}\)
Answer/Explanation
Ans:
A—Use the parallel axis theorem: \(I=I_{cm}+Mh^{2}\), where h is the distance between parallel axes. The rotational inertia through the object’s center of mass is (1/2)\(MR^{2}\). The distance between the two axes is R. So I = (1/2)\(MR^{2}\) + \(MR^{2}\) = (3/2)\(MR^{2}\).