If you could provide a step-by-step solution that would be much appreciated! Tha
ID: 2244871 • Letter: I
Question
If you could provide a step-by-step solution that would be much appreciated! Thanks
A horizontal circle platform rotates counterclockwise about its axis at the rate of 0.845 rad/s. You, with a mass of 70.7 kg, walk clockwise around the platform along its edge at the speed of 1.01 m/s with respect to the platform. Your 21.0-kg poodle also walks clockwise around the platform, but along a circle at half the flatform's radius and at half your linear speed with respect to the platform. Your 18.5-kg mutt, on the other hand, sits still on the platform at a position that is 3/4of the platform's radius from the center. Model the platform as a uniform disk with mass 90.9 kg and radius 1.97 m. Calculate the total angular momentum of the system.Explanation / Answer
Given
Circular platform rotates ccw 90.9 kg, radius 1.97 m, 0.845 rad/s
You 70.7 kg, cw 1.01 m/s, at r
Poodle 21.1 kg, cw 1.01/2 m/s, at r/2
Mutt 18.5 kg, 3r/4
You
Relative
w = v/r
=> 1.01/1.97 = 0.5126
Actual
w = 0.845 - 0.5126
= 0.3324
I = mr^2
= 70.7*1.97^2
= 274.38
L = Iw
= 274.38 *0.3324
= 91.20
Poodle
Relative
w = (1.01/2)/(1.97/2)
= 0.5126
Actual
w = 0.845 - 0.5126
= 0.3324
I = m(r/2)^2
= 21.1*(1.97/2)^2
= 20.47
L = Iw
= 20.47*0.3324
=6.80
Mutt
Actual
w = 0.845
I = m(3r/4)^2
= 18.5(3*1.97/4)^2
= 40.38
L = Iw
= 40.38*0.845
= 34.126
Disk
I = mr^2/2
= 90.9(1.97)^2/2
= 176.387
L = Iw
= 176.387*0.845
= 149.05
Total
L = 91.20 + 6.80+ 34.126+ 149.05
= 281.17 kg m^2/s