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 0.937 rad/s. You, with a mass of 72.7 kg, walk clockwise around the platform along its edge at the speed of 1.01 m/s with respect to the platform. Your 20.9-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 90.7 kg and radius 1.85 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular momentum of platform L1 = (1/2)*M*R^2*w

L1 = +(1/2)*90.7*1.85*1.85*0.937 = +145.432121375 kg m^2 /s

v1 = v + Rw = (-1.01)+(0.937*1.85) = + 0.72345 m/s

angular momentum of person L2 = m*v1*R

L2 = +72.7*0.72345*1.85 = +97.30040775 kg m^2 /s

v2 = v + Rw/2 = -(1.01/2)+((1.85*0.937)/2) = + 0.361725 m/s

angular momentum of poodle L3 = m*v2**R/2

L3 = +20.9*(0.361725)*(1.85/2) = +6.9930485625 kg m^2 /s

angular momentum of mutt L4 = I2*w = m*(3R/4)^2*w

L4 = +17.3*(1.3875*1.3875*0.937) = +31.206975328125 kg m^2 /s

Ltot = L1 L2 + L3 + L4 = +145.432121375 +97.30040775 +
6.9930485625 +31.206975328125 = +280.932553015625 kg m^2/s

counter clock wise direction

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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