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 0.961 rad/s. You, with a mass of 74.7 kg, walk clockwise around the platform along its edge at the speed of 1.05 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 17.1-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 90.3 kg and radius 1.97 m. Calculate the total angular momentum of the system.

Explanation / Answer

The angular momentum of the disk can be calculated by: Ang momentum = I*(ang velocity) where I is the rotational moment of inertia. For a disk it is: I = 1/2m*r^2 The angular momentum of the woman can be calculated by: Ang momentum = m*(ang velocity*r)*r First calculate the angular speed in rad/s: ang speed = (0.500rev/s)*(2*pi rad/rev) = 3.14 rad/s calculate the angular momentum of the disk: ang momentum disk = I*(ang vel) = (0.5)*(110kg)*(4.00m)^2*(3.14rad/s) = 2,763 kg-m^2/s ang momentum woman = (50kg)*(3.14rad/s*(4.00m))*(4.00m)) = 2,512 kg-m/s^2 So the total angular momentum is: ang momentum = 2,763 kg-m^2/s + 2,512 kg-m/s^2 = 5,275 kg-m^2/s Hope this helps

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