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Physics / Physics: Principles with Applications 6 / Chapter 8 / Problem 36P

Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli

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A teenager pushes tangentially on a small hand-driven merry-go-round and is able to

Chapter 8, Problem 36P

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QUESTION:

Problem 36P

A teenager pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?

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QUESTION:

Problem 36P

A teenager pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?

ANSWER:

Solution 36P:

Step 1 of 3:-

Here we have to find the torque.

The frequency it achieved is: $\nu{}=15\ rpm$ .

So, ${\omega{}}_{f}=15\times{}\frac{2\pi{}}{60}=1.570\ rad/s$ .

The initial angular acceleration was: ${\omega{}}_{i}=0$

The angular velocity changed in 10 s.

The angular acceleration is: $\alpha{}=\frac{\Delta{}\omega{}}{\Delta{}t}=1.570/10=0.157\ rad/{s}^{2}$ .

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