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 10m/s?
(a) 1:1, kinetic energy is frame independant
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I’d like to ask this question from Rolling Motion topic in chapter System of Particles and Rotational Motion of Physics – Class 11
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The correct choice is (b) 3:1
Easiest explanation: The kinetic energy of a pure rolling disc as seen from the ground frame is given by: 1/2MV^2 + 1/2Iw^2.
I = MR^2/2 w = V/R
∴ 1/2MV^2 + 1/2Iw^2 = 1/2MV^2 + 1/4MV^2 = 3/4MV^2.
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 = 1/2Iw^2 = 1/4MV^2.
∴ Ratio = (3/4MV^2) / (1/4MV^2)