Question

A hoop, a solid sphere, and a solid cylinder all have a mass of 2.2 kg and a radius of 6.5

cm. Each one is placed at the top of an inclined plane that is 1.2 meters long and inclined at
an angle of 30 degrees and released from rest. Which object has the largest rotational kinetic energy when it reaches the bottom of the inclined plane?

A. The hoop

B. The solid sphere

C. The solid cylinder

D. The rotational kinetic energy is the same for all three objects

E. It cannot be determined with the information given

Answer 1

The student's question pertains to the comparison of rotational kinetic energies among a hoop, solid sphere, and solid cylinder. Without the angular velocity, we cannot determine which has the most rotational kinetic energy, because the moments of inertia differ.

Step-by-step explanation:

The student is asking about the rotational kinetic energy of different objects with the same mass and radius. Rotational kinetic energy is the energy an object possesses due to its rotation and is given by the formula ½Iω², where I is the moment of inertia and ω is the angular velocity.

For objects such as a hoop, a solid sphere, and a solid cylinder, the moments of inertia are different: a hoop has I = MR², a solid sphere has I = 2/5 MR², and a solid cylinder has I = 1/2 MR². Because of these different moments, the rotational kinetic energies will differ if they are spinning at the same angular velocity. The information provided in the question is insufficient to determine which object has the greatest rotational kinetic energy without additional details such as the angular velocity of the objects.