A disc is undergoing pure rolling motion on a flat surface. The radius of the disc is 5cm & velocity of centre of mass is 10m/s. What is the ratio of kinetic energy as seen from the ground frame to a frame moving along the disc with a speed of 10 m/s?
Answer & explanation
Correct answer: option 1
The kinetic energy of a pure rolling disc as seen from the ground frame is given by: 1/2MV2 + 1/2Iw2.
I = MR2/2 w = V/R
∴ 1/2MV2 + 1/2Iw2 = 1/2MV2 + 1/4MV2 = 3/4MV2.
Kinetic energy as seen from the moving frame will only be the energy due to rotation about the disc’s axis.
∴ Kinetic energy from moving frame = 1/2Iw2 = 1/4MV2.
∴ Ratio = (3/4MV2) / (1/4MV2)
= 3:1.