A Sapling Learning A horizontal circular plaforma rotates counterclockwise about

Question

A Sapling Learning A horizontal circular plaforma rotates counterclockwise about its axis at the rate of 0.805 rad/s. You, with a mass of 70.3 kg, walk clockwise around the platform along its edge at the speed of 1.07 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 latforms radius and at half your linear speed with respect to the platform. Your 19.1-kg mutt, on the other and, 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 91.7 kg and radius 1.97 m. Calculate the total angular momentum of the system. Number kg. mi s Tools x 10

Explanation / Answer

for you M = 70.3 kg, w = 0.805 rad/s , v= 1.07 m/s,

poodle m = 21.1 kg , mutt m = 19.1 kg, r1 = 3r/4

m = 91.7 kg

r = 1.97 m

for you

relative angular velocity w = v/r

w = 1.07/1.97 = 0.543 rad/s

Actual anular velocity w = 0.805 -0.543

w = 0.262 rad/s

moment of inertia of circular platform I = Mr^2

angular momentum L = Iw

L = 70.3*1.97^2*0.262

L = 71.48 kg.m^2/s

Poddle

relative w = (1.07/2)/(1.97/2) = 0.543 rad/s

actual w = 0.805 -0543 = 0.262rad/s

moment inertia of puddle I = m(r/2)^2

L = 21.1*(1.97/2)^2*0.262

L = 5.364 kg.m^2/s

for mutt

w = 0.805rad/s

I = m(3r/4)^2

L = (19.1)(3*1.97/4)^2*0.805

L = 33.56 kg.m^2/s

for Disk

I = 0.5mr^2/2

L = 0.5*91.7*(1.97)^2*0.805 = 143 kg.m^2/s

Total L = 71.48 +5.364+33.56+143

L =253.4 kg.m^2/s

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