suddenly step A 50 m diamater merry-go-round is rotating frely with an angular v

Question

suddenly step A 50 m diamater merry-go-round is rotating frely with an angular velocity of o.80 rad/s. Its total moment of inertia is 1800 kp-, Four people standing on the ground, each of 60 kg mass, orto the elp of the merry#round. (a) What is the anglar velocity of the merry go-round now? rad/s (b) Assume that the people were on i ini the mery go round (en the nular valodty is 0.0 rdls) and then jmped ot i radial diection (relative to the mary go-round) What wuld be the anglar valocity of rad/s

Explanation / Answer

Given that,

diameter = 5 m

radius, r = 5 / 2 = 2.5 m

initial angular velocity, wi = 0.8 rad/s

total moment of inertia, l = 1800 kg.m^2

mass, m = 60 kg

(a)

moment of inertia when they steps onto the edge,

l' = l + 4mr^2

l' = 1800 + 4*60*(2.5)^2 = 3300 kg.m^2

From conservation of angular momentum,

l1*w1 = l2*w2

1800*0.8 = 3300*wf

wf = 0.436 rad/s

(b)

When people jumped off in a radial direction,

There is no external torque working.

so, wi = wf = 0.80

w = 0.80 rad/s

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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