A spherical shell of radius 1.59 cm and a sphere of radius 7.22 cm are rolling w

Question

A spherical shell of radius 1.59 cm and a sphere of radius 7.22 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?

A spherical shell of radius 1.59 cm and a sphere of radius 7.22 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? Number shl sph

Explanation / Answer

KE = 0.5*I*W^2

where I = moment of inertia

I(shell) = 2*m*r^2 / 3  

I(sphere) = 2*m*r^2 / 5

now KE(shell) = KE(sphere)

0.5*I(shell)*Wsh^2 = 0.5*I(sphere)*Wsp^2

=> 2*m*(0.0159)^2*Wsh^2 / 3 = 2*m*(0.0722)^2*Wsp^2 / 5

=> Wsh^2 / Wsp^2 = 0.6*(0.0722/0.0159)^2

=> Wsh/Wsp = 3.516  

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