Question

A coin is rolling in a plane surface .what fraction of its total kinetic energy is rotational

Answer 1

In case of rolling without slipping the angular velocity (ω) and the velocity of centre of mass (v) are related as: v = Rω.

Moment of inertia of the coin (disc), I = 1/2mr​2

Total kinetic energy, K = Translational kinetic energy + Rotational kinetic energy

 

or, K = 1/2 mv2​ + 1/2 Iω2

 

We can write rotational kinetic energy as: 

 

1/2 Iω​2 = (1/2 )×(1/2 mr2​) (ω​2) = 1/4 m (rω)2 = 1/4 mv​2 

 

Thus,

 

K total = Kt + Kr 

 

2Kr = Kt

 

Ktotal = 3 Kr

 

Fraction of rotational kinetic energy

 

Kr/3 Kr = 1/3

Answer 2

Explanation:

KE rotational=1/4mv^2

total KE= 3/4mv^2

fraction of total kE is rotational

KE rotational ÷total KE = 1/3