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 0.851 rad/s. You, with a mass of 73.1 kg, walk clockwise around the platform along its edge at the speed of 1.05 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 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 1.83 m. Calculate the total angular momentum of the system.

Explanation / Answer

Moment of inertia of the platform,

I =(1/42m*r^2,

=(1/2)*90.3*1.83^2 =151.20 kg*m^2

Angular speed of the platfrom,

w=0.851 rad/s (counter clockwise)

Momentum of inertia of the man,

I1=m1*r1^2=73.1*1.83^2

=244.8 kg*m^2

Speed of man = w*r-v=.851*1.83-1.05 =.507 m/s

Angular speed of the man.

w1= .507/r =.207 rad/s

Moment of inertia of poddle,

I2 = m2*r2^2

= 20.3*(1.83/2)^2

=16.99 kg*m^2

Speed of the poddle = .851*(1.83/2)-.507/2=0.779-.254 =.525m/s

angular speed of poddle w2= .254/(r/2) =.573 rad/s

Moment of inertia of mut

I3=m3*r3^2=17.1((3/4)*1.83) =23.47 kg*m^2,

Angular speed w3=.851 rad/s

Total angular momentum,

= I1w1+I2w2+I3w3+Iw

=220.03kg*m^2/s

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