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A teenager pushes tangentially on a small hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 20 rpm in 8.0s. Assume the

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asked 2021-04-20
A teenager pushes tangentially on a small hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 20 rpm in 8.0s. Assume the merry-go-round is auniform disk of radius 2.0m and has a mass of 600kg, and twochildren (each with a mass of 20kg) sit opposite each other on theedge.
A) Calculate the torque required to produce theacceleration, neglecting frictional torque.
B) What force is required at the edge?

Answers (1)

2021-04-22

The initial angular frequency \(\displaystyle\omega_{{{0}}}={0}\)
The Final angular frequency \(\displaystyle\omega_{{{f}}}={20}{r}\pm\)
\(\displaystyle={20}\cdot{\left({2}\frac{\pi}{{60}}\right)}{r}{a}\frac{{d}}{{s}}\)
The time taken t = 8s
The radius of the merry-go-round R = 2m
Mass of merry-go-round M = 600kg
Mass of child m = 20kg
Therefore the angular acceleration \(\displaystyle\alpha=\triangle\frac{\omega}{\triangle}{t}\)
The Torque required \(\displaystyle{T}={I}_{{{s}{y}{s}{t}{e}{m}}}\cdot\alpha\)
\(\displaystyle={\left({I}_{{{m}{e}{r}{r}{y}}}+{I}_{{chi{l}{d}{r}{e}{n}}}\right)}\cdot\alpha\)
\(\displaystyle={\left[{\left(\frac{{1}}{{2}}\right)}{M}_{{{m}{e}{r}{r}{y}}}{R}^{{{2}}}+{2}{m}_{{chi{l}{d}}}{R}^{{{2}}}\right]}\cdot\alpha\)
substitute the values and calculate the Torque.
b) The Force required at the edge is calculated from the torque
\(\displaystyle{T}={F}_{{{p}{e}{r}{p}{e}{n}{d}{i}{c}\underline{{a}}{r}}}\cdot{R}{a}{d}{i}{u}{s}\)
Or \(F=\frac{t}{R}\)

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