A particularly large playground merry-go-round is essentially a uniform solid di

Question

A particularly large playground merry-go-round is essentially a uniform solid disk of mass 3M and radius R that can rotate with no friction about a central axis. You, with a mass M, are a distance of R/2 from the center of the merry-go-round, rotating together with it at an angular velocity of 2.20 rad/s clockwise (when viewed from above). You then move to the outside of the merry-go-round so you are a distance R from the center, still rotating with the merry-go-round. Consider you and the merry-go-round to be one system.

(a) When you reach the outer edge of the merry-go-round, what is the angular velocity of the you and merry-go-round system?
rad/s

(b) You then start running around the outer edge of the merry-go-round. At what angular speed would you have to run to make the merry-go-round alone come to a complete stop?
rad/s

Explanation / Answer

a) we will conserve angular momentum = Iw

2.20 ( I disk + I man) = w ( I disk +I man)

2.20 [ 1/2 (3M) (R^2) + M (R^2/4) ] = w (1/2 (3M) (R^2) + MR^2)

2.20 ( 3/2 + 1/4) = w ( 3/2 + 1)

w= 3.85/ 2.5= 1.54 rad/s

b)

in this case it should be an inelastic collsion, man shoudl run opposite to the direction of merry-go -around

( 1/2 3MR^2 ) W = ( MR^2) (w)

( 3/2) (1.54)= w

w=angular speed of man should be 1.5 times of the angular speed of disk = 2.31 rad/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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