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 0.951 rad/s. You, with a mass of 73.1 kg, walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 21.1-kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 19.1-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 91.1 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular momentum of platform= Iw = MR^2 * 0.951 /2 =91.1*1.89^2 * 0.951/2 = 154.73 Kgm^2 rad/sec

Angular momentum of person = Iw = MR^2*w = 73.1*1.89*1.89*1.486 = -388.025 Kgm^2 rad/sec

Anular meomentum of poddle = Iw = MR^2*w = 21.2*1.89*1.89 *1.486 */4 =- 28.133 Kgm^2 rad/sec

Angular momentum of mutt = Iw = MR^2*w = 19.1*9*1.89*1.89 *0.951 */16 = 36.497 Kgm^2 rad/sec

Net angular momentum = 154.73 -388.025 - 28.133 + 36.497 = -224.931 Kgm^2 rad/sec {counter clockwise

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