Question

A coin is rolling on a plane surface.what fraction of its total K.Eis rotational

Answer 1

Answer:

Explanation:

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.

Hope it helps you.

Answer 2

Answer: 1/3

Explanation:

a coin can be considers as a solid disc

moment of inertia ( I ) = MR² / 2

radius of gyration (K) = √R / √2

rotational kinetic energy = 1/2 * I * ω²           [ ω = v / R ]

total energy = 1/2 mv² [ 1 + k²/r² ]

fraction =  [ 1/2 * I * ω² ]  ÷ [ 1/2 mv² [ 1 + k²/r² ] ]  = 1/3