Question

In: Physics

A spherical shell of radius 2.84 cm and a sphere of radius 7.97 cm are rolling...

A spherical shell of radius 2.84 cm and a sphere of radius 7.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the spherical shell\'s angular speed to the sphere\'s angular speed be?

Expert Solution

Mass of the spherical shell = M₁

Radius of the spherical shell = R₁ = 2.84 cm = 0.0284 m

Moment of inertia of the spherical shell = I₁ = 2M₁R₁²/3

Angular speed of the spherical shell = ₁

Speed of the spherical shell = V₁ = ₁R₁

Kinetic energy of the spherical shell = KE₁

Mass of the sphere = M₂

Radius of the sphere = R₂ = 7.97 cm = 0.0797 m

Moment of inertia of the sphere = I₂ = 2M₂R₂²/5

Angular speed of the sphere = ₂

Speed of the sphere = V₂ = ₂R₂

Kinetic energy of the sphere = KE₂

The spherical shell and the sphere have same mass.

M₁ = M₂

The spherical shell and the sphere have same kinetic energy.

KE₁ = KE₂

Ratio of the spherical shell's angular speed to the sphere's angular speed = 2.572

genius_generous answered 7 months ago

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