A horizontal circular platform rotates counterclockwise about its axis at the ra

Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.861 rad/s. You, with a mass of 65.1 kg, walk clockwise around the platform along its edge at the speed of 1.17 m/s with respect to the platform. Your 20.3-kg poodle also walks clockwise around the platform, but along a circle at halt the platform?s radius and at half your linear speed with respect to the platform. Your 17.3-kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform?s radius from the center. Model the platform as a uniform disk with mass 90.7 kg and radius 1.91 m. Calculate the total angular momentum of the system.

Explanation / Answer

Angular velocity = linear velocity * radius of curvature

Angular Momentum of the disk is = m? = 90.7 *0.861 = 78.0927 Nms

Actual angular velocity of the person = (1.17 * 1.91) + (0.861) = 3.0957 rad/s

Angular moment of Person = 65.1 * 3.0957 = 201.53007 Nms

Actual angular velocity of the poodle = [(1.17/2) *(1.91/2)] + 0.861 = 2.401 rad/s

Angular momentum of poodle = 20.3 * 2.401 = 48.7403 Nms

Actual angular velocity of the mutt = 0.861 rad/s

Angular momentum of mutt = 17.3 * 0.861 = 14.8953 Nms

Adding all angular momentums

Angular momentum of system = 343.26 Nms or kgm2/s

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