horizontal circular platform rotates counterclockwise about its axis at the rate
ID: 1499184 • Letter: H
Question
horizontal circular platform rotates counterclockwise about its axis at the rate of 0.835 rad/s. You, with a mass of 65.9 kg, walk clockwise around the platform along its edge at the speed of 1.01 m/s with respect to the platform. Your 20.5-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 17.5-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 91.5 kg and radius 1.81 m. Calculate the total angular momentum of the system.
Explanation / Answer
Circular platform rotates ccw 91.5 kg, radius 1.81 m, 0.835 rad/s
You 65.9 kg, cw 1.01 m/s, at r
Poodle 20.5 kg, cw 1.01/2 m/s, at r/2
Mutt 17.5 kg, 3r/4
The total angular momentum is defined by the addition of all the momentums
Let's start with you
Relative
= v/r = 1.01/1.81 = 0.5580
Absolute
= 0.835 - 0.5580= 0.277
Knowing your angular speed we can proceed with the Inertia and momentum
I = mr^2 = 65.9*1.81^2 = 215.89
L = I = 234.24*0.3408 = 59.801
Poodle
Relative
= (1.01/2)/(1.81/2) = 0.5580
Absolute
= 0.835 - 0.5580 = 0.277
Inetia and momentum
I = m(r/2)^2 = 20.5*(1.81/2)^2 = 16.79
L = I = 16.79*0.277 = 4.6508
Mutt
Absolute
= 0.835
Inertia and momentum
I = m(3r/4)^2 = 17.5(3*1.81/4)^2 = 32.24
L = I = 32.24*0.835= 26.9280
Disk
I = mr^2/2 = 91.5(1.81)^2/2 = 152.17
L = I = 152.17*0.835 = 127.06
Total
L = 59.80 + 4.65 + 26.92 + 127.06 = 218.43 kg m^2/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.