Question

A ring rolls on A plane surface.the fraction of its total energy associated with its rotation is​

Answer 1

Answer:

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

>>Kr = 1/3

Explanation:

Given:

A ring rolls on A plane surface.the fraction of its total energy associated with its rotation is​

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

Solution:

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