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 0.841 rad/s. You, with a mass of 73.7 kg, walk clockwise around the platform along its edge at the speed of 1.13 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 platform's radius and at half your linear speed with respect to the platform. Your 18.7-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 92.1 kg and radius 1.95 m. Calculate the total angular momentum of the system.

Explanation / Answer

given
mass of platform, M = 92.1 kg
rqadius of platform, R = 1.95 m
angular velocity of platform, W = 0.841 rad/s

mass of person, m = 73.7 kg, at edge,
speed of man relative to platform = 1.13 m/s
so, angular spee dof man relative to the rotating platform, = 1.13/1.95 = 0.579 rad/s ( clockwise)
angular speed of man , w = angular speed of man wrt platform - angular speed of platform wrt ground = -0.579 - 0.841 = -1.42 rad/s

similiarly
mass of poodle, m' = 21.1 kg, at R/2
poodle's linear speed wrt platform = 1.13/2 m/s
so angular speed of poodle, w' = 1.13*2/2*1.95 - 0.841 = -1.42 m/s

and
mass of mutt, m" = 18.7 kg, at 3R/4
w" = 0.841 rad/s

net angular momentum of the system = 0.5MR^2*W + mR^2*w + m'*R^2*w'/4 + m"*9*R^2*w"/16 = (0.5M*W + m*w + m'w'/4 + m"*9*w"/16)R^2 = -245.528114203125 kg m^2 rad/s [ clockwise direction]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.