A playground merry-go-round has a radius of 4.30m and a moment of inertia of 255

Question

A playground merry-go-round has a radius of 4.30m and a moment of inertia of 255kg?m2 and turns with negligible friction about a vertical axle through its center.

Part A

A child applies a 25.0N force tangentially to the edge of the merry-go-round for 20.0s . If the merry-go-round is initially at rest, what is its angular velocity after this 20.0s interval?

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Part B

How much work did the child do on the merry-go-round?

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Part C

What is the average power supplied by the child?

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A playground merry-go-round has a radius of 4.30m and a moment of inertia of 255kg?m2 and turns with negligible friction about a vertical axle through its center.

Part A

A child applies a 25.0N force tangentially to the edge of the merry-go-round for 20.0s . If the merry-go-round is initially at rest, what is its angular velocity after this 20.0s interval?

? =   rad/s  

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Part B

How much work did the child do on the merry-go-round?

W =   J  

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Part C

What is the average power supplied by the child?

P =   W  

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Explanation / Answer

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A playground merry-go-round has a radius of 4.4 m and a moment ofinertia of 245 kg.m^2 and turns with negligible friction about avertical axle through its center. (a) A child applies a 25 N forcetangentially to the edge of the merry-go-round for 20 s. If themerry-go-round is initially at rest, what is its angular velocityafter this 20 s interval? (b) How much work did the child do on themerry-go-round? (c) What is the average power supplied by thechild?

Answer

(a) Torque = force * r = 25 * 4.4 =   110 N-m

.

      acceleration = torque / I = 110 / 245 =   0.44898rad/s2

.

   final angular velocity = acceleration* time = 0.44898 * 20 =   8.98rad/sec

.

(b) work = torque * angular distance = torque *avg speed * time = torque * (final speed / 2) * time=

.

              =   110 * (8.98/2) * 20 = 9878 Joules

.

(c) avg power = work / time = 9878 / 20 =    494Watts

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