Rotational Kinetic Energy AP Physics C Mechanics MCQ – Exam Style Questions etc.
Rotational Kinetic Energy AP Physics C Mechanics MCQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Question
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.
If the plane is frictionless, what is the speed v of the center of mass of the sphere at the bottom of the incline?
(A)\(\sqrt{2gh}\)
(B)\(\frac{2Mgh}{I}\)
(C)\(\frac{2Mghr^2}{I}\)
(D)\(\sqrt{\frac{2Mghr^2}{I}}\)
(E)\(\sqrt{\frac{2Mghr^2}{I+Mr^2}}\)
Answer/Explanation
Ans:A
Question
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.
If the plane has friction so that the sphere rolls without slipping, what is the speed \(v_{cm}\) of the center of mass at the bottom of the incline?
(A)\(\sqrt{2gh}\)
(B)\(\frac{2Mgh}{I}\)
(C)\(\frac{2Mghr^2}{I}\)
(D)\(\sqrt{\frac{2Mghr^2}{I}}\)
(E)\(\sqrt{\frac{2Mghr^2}{I+Mr^2}}\)
Answer/Explanation
Ans:E
Question
A particle is moving in a circle of radius 2 meters according to the relation θ = 3t2+ 2t, where θ is measured in radians and t in seconds. The speed of the particle at t = 4 seconds is
(A) 13 m/s (B) 16 m/s (C) 26 m/s (D) 52 m/s (E) 338 m/s
Answer/Explanation
Ans:D
Solution: ω = dθ/dt = 6t + 2; v = ωr
Question
In which of the following diagrams is the torque about point O equal in magnitude to the torque about point X in the diagram above? (All forces lie in the plane of the paper.)
Answer/Explanation
Ans:C
Solution: τX = Fl; τO = FOLO sin θ, solve for the correct combination of FO and LO