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 0.969 rad/s. You, with a mass of 66.5 kg, walk clockwise around the platform along its edge at the speed of 1.03 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 17.7-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 91.3 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

mass of the disk, m=91.3 kg

radius of the disk r=1.89 m

angular speed of circular platform, w=0.969 rad/sec

mass of the person m1=66.5 kg and speed v1=1.03 m/sec at r1=1.89 m

mass of the poodle m2=20.7 kg and speed v2=v1/2=1.03/2 =0.515 m/sec at r2=r/2

r2=1.89/2=0.945 m

mass of the mutt m3=17.7 kg and speed v3=v1 and at r3=3/4*r1

total angular momentum is

L=L1+L2+L3+L4

here,

angular momentum of person is,L1=I1*w1

L1=m1*r1^2*(w-v1/r1)

L1=66.5*(1.89)^2*(0.969-1.03/1.89)

L1=100.725 kg.m^2/sec

angular momentum of poodle is,L2=I2*w2

L2=m2*r2^2*(w1-v2/r2)

L2=m2*(r1/2)^2*(w1-(v1/2)/(r1/2))

L2=m2*(r1/2)^2*(w1-v1/r1)

L2=20.7*(1.89/2)^2*(0.969-1.03/1.89)

L2=7.84 kg.m^2/sec

angular momentum of mutt is,L3=I3*w3

L3=m3*r3^2*(w3)

L3=17.7*((3/4)*1.89)^2*(0.969)

L3=34.462 kg.m^2/sec

angular momentum of disk is,L4=I4*w4

L4=1/2*m*r^2*(w)

L4=1/2*91.3*(1.89)^2*(0.969)

L4=158.01 kg.m^2/sec

now,

total angular momentum is,

L=L1+L2+L3+L4

L=(100.725+7.84+34.462+158.01)

L=301.04 kg.m^2/sec

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