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 .827 rad/s. You, wth a mass of 70.7 kg, walk clockwise around the platform along its edge at the speed of 1.15 m/s with respect to the platform. Your 20.3-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 18.5-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 90.1 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)

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