A horizontal circular platform (M = 145.1 kg, r = 3.25 m) rotates about a fricti

Question

A horizontal circular platform (M = 145.1 kg, r = 3.25 m) rotates about a frictionless vertical axle. A 81.3-kg student walks slowly from the rim of the platform toward the center. The angular velocity of the system is 1.1 rad/s when the student is at the rim. Find the angular velocity of the system when the student is 2.67 m from the center.

A horizontal circular platform (M = 145.1 kg, r = 3.25 m) rotates about a frictionless vertical axle. A 81.3-kg student walks slowly from the rim of the platform toward the center. The angular velocity of the system is 1.1 rad/s when the student is at the rim. Find the angular velocity of the system when the student is 2.67 m from the center.

Explanation / Answer

I1 = 0.5*M*r^2+m*r^2 = (0.5*145.1*3.25^2) + (81.3*3.25^2) = 1625.041


W1 = 1.1 rad/s

I2 = 0.5*M*r^2 + m*r1^2 = (0.5*145.1*3.25^2) + (81.3*2.67^2)= 1345.889

W2 = ?

I1*W1 =I2*W2

W2 = (1625.041*1.1)/(1345.889 ) = 1.328 rad/s

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