A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane?
A) 2.04 m/s
B) 3.53 m/s
C) 4.07 m/s
D) 5.71 m/s
E) 6.29 m/s

Question

Quizplus · Accepted Answer

Let's use conservation of energy here. The initial potential energy of the disk is converted to both translational and rotational kinetic energy. Therefore we can write:
Mgh = (1/2)MV^2 + (1/2)Iω^2
where M is the mass of the disk, h is the height of the inclined plane, V is the velocity of the disk, I is the moment of inertia of the disk, and ω is the angular velocity of the disk.
We know that the disk is rolling without slipping. Therefore we can relate the linear velocity to the angular velocity as V = Rω, where R is the radius of the disk.
Also, for a solid disk, the moment of inertia is (1/2)MR^2.
Substituting all these values into the energy equation and rearranging, we get:
V = sqrt(2gh/3) = 4.07 m/s
Therefore, the answer is (C).

A Solid Disk Is Released from Rest and Rolls Without