A scientist is performing an experiment involving a merry-go-round and some larg

Question

A scientist is performing an experiment involving a merry-go-round and some large weights. She begins by stacking 8 weights on the center of the merry-go-round, then spinning it to give it some initial angular velocity. She would like to place the weights equidistant from the center of the merry-go-round such that it slows to 2/3 of its initial angular velocity. If the merry-go-round is 800 kg, and each weight is 35 kg, at what radius (how far from the center of the ride) should she place each weight, in relation to the radius of the merry-go-round?

Explanation / Answer

here,

mass of weight added , m1 = 35 kg

mass of merry go round , m2 = 800 kg

w = 2/3 * w0

let the distance at which the weights are placed be x and radius be r

initial moment of inertia , I0 = 0.5 * m2 * r^2

final moment of inertia , I = 0.5 * m2 * r^2 + m1 * x^2

using conservation of angular momentum

I0 * w0 = I * w

( 0.5 * m2 * r^2 ) = (0.5 * m2 * r^2
+ m1 * x^2) * 2/3

3 * ( 0.5 * 800 * r^2) = 2 * ( 0.5 * 800 * r^2 + 35 * x^2)

400 * r^2 = 70 * x^2

x = 2.39 * sqrt(r)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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