Question

In: Physics

A sphere of radius 2.09 cm and a spherical shell of radius 6.97 cm are rolling...

A sphere of radius 2.09 cm and a spherical shell of radius 6.97 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 sphere\'s angular speed to the spherical shell\'s angular speed be? Please provide a clear explanation. I have tried to look this problem u, but I was unable to understand exactly how the solution was found.

Expert Solution

Radius of sphere = R₁ = 2.09 cm = 0.0209 m

Radius of spherical shell = R₂ = 6.97 cm = 0.0697 m

Both the objects have same mass.

Mass of the sphere = Mass of the spherical shell = M

Moment of inertia of the sphere = I₁ = 2MR₁²/5

Moment of inertia of the spherical shell = I₂ = 2MR₂²/3

Angular speed of the sphere = ₁

Angular speed of the spherical shell = ₂

Both the objects are rolling without slipping.

Velocity of the sphere = V₁ = ₁R₁

Velocity of the spherical shell = V₂ = ₂R₂

Total kinetic energy of the sphere = KE₁

Total kinetic energy of the spherical shell = KE₂

KE₁ = MV₁²/2 + I₁₁²/2

KE₂ = MV₂²/2 + I₂₂²/2

Both the objects have same total kinetic energy.

KE₁ = KE₂

Ratio of the sphere's angular speed to the spherical shell's angular speed = 3.64

genius_generous answered 5 months ago

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