A cylinder with moment of inertia 20.1 kg m 2 rotates with angular velocity 11 r

Question

A cylinder with moment of inertia 20.1 kg m2 rotates with angular velocity 11 rad/s on a frictionless vertical axle. A second cylinder, with moment of inertia 21.4 kg m2, initially not rotating, drops onto the first cylinder and remains in contact. Since the surfaces are rough, the two eventually reach the same angular velocity.

Calculate the final angular velocity.

Answer in units of rad/s

A cylinder with moment of inertia 20.1 kg m^2 rotates with angular velocity 11 rad/s on a frictionless vertical axle. A second cylinder, with moment of inertia 21.4 kg m^2, initially not rotating, drops onto the first cylinder and remains in contact. Since the surfaces are rough, the two eventually reach the same angular velocity. Calculate the final angular velocity. Answer in units of rad/s

Explanation / Answer

using energy balance,

I1w12 = I2w22

w2= sqrt[20.1*112/(20.1+21.4)] =7.65 rad/s

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