Stacy exerts a force of 900 N at the edge of the 50.0 kg merry-go-round, which h

Question

Stacy exerts a force of 900 N at the edge of the 50.0 kg merry-go-round, which has a 1.50 m radius. Calculate the angular acceleration produced: (a) when no one is on the merry-go-round; (b) when two 25.0 kg kids sit 1.20 m from the center and another 35.5 kg kid sits 1.45 m from the center. Consider the merry-go-round to be a unifrom disk with negligible retarding friction. (Imgs= 1/2 MR^2) (Ikid=MR^2)

Stacy exerts a force of 900 N at the edge of the 50.0 kg merry-go-round, which has a 1.50 m radius. Calculate the angular acceleration produced: (a) when no one is on the merry-go-round; (b) when two 25.0 kg kids sit 1.20 m from the center and another 35.5 kg kid sits 1.45 m from the center. Consider the merry-go-round to be a unifrom disk with negligible retarding friction. (Imgs= 1/2 MR^2) (Ikid=MR^2)

Explanation / Answer

since the merry go round is solid,

so we need to treat it like a disk whose moment of inertia is 0.5MR^2

a)balancing torques,

0.5*50*1.5^2*x=F.r

or 0.5*50*1.5^2*x=900*1.5

or x=24 rad/s^2

b)balancing troques,

(0.5*50*1.5^2+25*1.2^2*2+35*1.45^2)*x=900*1.5

or x=6.69 rad/s^2

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