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? |
3:1 1:1, kinetic energy is frame independent 1:3 2:1 |
3:1 |
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. |