Question

In: Physics

Two balls (solid spheres) have the same radius and the same rotational kinetic energy. If the...

Two balls (solid spheres) have the same radius and the same rotational kinetic energy. If the ratio of their masses is

m₁

m₂

=

4

1

, what is the ratio of their angular velocities?

Expert Solution

Mass of the first ball = m₁

Radius of the first ball = R₁

Moment of inertia of the first ball = I₁ = 2m₁R₁²/5

Angular velocity of the first ball = ₁

Rotational kinetic energy of the first ball = E₁

Mass of the second ball = m₂

Radius of the second ball = R₂

Moment of inertia of the second ball = I₂ = 2m₂R₂²/5

Angular velocity of the second ball = ₂

Rotational kinetic energy of the second ball = E₂

Ratio of the masses of the balls = m₁/m₂ = 4/1

The balls have the same radius.

R₁ = R₂

The balls have the same rotational kinetic energy.

E₁ = E₂

Ratio of the angular velocities of the balls is given by,

genius_generous answered 2 hours ago

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