Rotational Kinetic Energy AP Physics 1 MCQ – Exam Style Questions etc.
Rotational Kinetic Energy AP Physics 1 MCQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Exam Style Practice Questions,Rotational Kinetic Energy AP Physics 1 MCQ
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
The center of mass of a cylinder of mass m, radius r, and rotational inertia \(I = \frac{1}{2} mr^2\) has a velocity of \(v_{cm}\) as it rolls without slipping along a horizontal surface. It then encounters a ramp of angle \(\theta \), and continues to roll up the ramp without slipping.
Now the cylinder is replaced with a hoop that has the same mass and radius. The hoop’s rotational inertia is \(mr^2\). The center of mass of the hoop has the same velocity as the cylinder when it is rolling along the horizontal surface and the hoop also rolls up the ramp without slipping. How would the maximum height of the cylinder?
(A) The hoop would reach a greater maximum height than the cylinder.
(B) The hoop and cylinder would reach the same maximum height.
(C) The cylinder would reach a greater maximum height than the hoop.
(D) The cylinder would reach less than half the height of the hoop.
(E) None of the above.
Answer/Explanation
Ans: A
Again we will use the Law of Conservation of Energy. The easiest way to determine which object will reach a greater height is to determine which object has more kinetic energy as it rolls along the horizontal surface. If both the cylinder and the hoop have the same velocity then the hoop will have more total kinetic energy because it has a greater rotational inertia. The calculation at the top of the next page shows the calculation for the height which also shows that the hoop reaches a greater height.
While both (A) and (D) indicate that the hoop reaches a greater maximum height than the cylinder, (D) is incorrect as the cylinder reaches 3/4 the height of the hoop.