Map Sapling Learning macmillan learning A horizontal circular platform rotates c

Question

Map Sapling Learning macmillan learning A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.801 rad/s. You, with a mass of 72.9 kg, walk clockwise around the platform along its edge at the speed of 1.19 m/s with respect to the platform. Your 20.9-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 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 91.9 kg and radius 1.83 m. Calculate the total angular momentum of the system Number 193 kg. mi

Explanation / Answer

The angular speed of the plateform w.r.t ground = 0.801 rad/s

The angular speed of the person with respect to the plateform = 1.19/1.83 = 0.65 rad/sec

The angular speed of the person w.r.t ground = 0.801-0.650 = 0.151 rad/s

The angular speed of the poodle with respect to the plateform = (1.19/2)/(1.83/2) = 0.65 rad/sec

The angular speed of the poodle w.r.t ground = 0.801-0.650 = 0.151 rad/s

The angular speed of the mutt w.r.t ground = 0.801 rad/s

The net angular momentum = summation of ang. momentum of all objects.

(angular momentum is 0.5 I omega^2, where I is moment of intertia and omega is the angular speed)

Angular momentum = 0.5*(91.9*1.83^2/2)*0.801 + 0.5*(72.9*1.83^2)*0.151^2+0.5*20.9*(1.83/2)^2*0.151^2+0.5*17.3*(1.83*3/4)^2*0.801^2 = 75.067 kg m^2/s^2

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