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 0.901 rad/s. You, with a mass of 74.5 kg, walk clockwise around the platform along its edge at the speed of 1.11 m/s with respect to the platform. Your 20.7-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 1.85 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular momentum is L = m*v*r*sin(theta) = I*w

I is the moment of inertia and w is the angular velocity

relation between linear speed and angular speed is v = r*w

For counterclockwise direction the L is positive and for clockwise L is negative

angulr momentum of the system L = angular momentum of the (platform + man + poodle + mutt)

L = L1 + L2 + L3 + L4

L = (I1*w1)-(m1*v1*r)-(m2*v2*r)+(I2*w2)

L = (0.5*91.9*1.85^2*0.901)-(74.5*1.11*1.85)-(20.7*(1.11/2)*(1.85/2))+(17.3*(3*1.85/4)^2*0.901)

L = 8.09 kg-m^2/sec

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