Question

a playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.600 rev/s. what is its angular velocity (in rev/s) after a 21.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.

Answer 1

The value of the final angular velocity = 0.44 rev/s

How to calculate the angular velocity?

Let Initial angular momentum = $L_{i}$

Let Final angular momentum = $L_{f}$

Here, mass of merry go round = $m_{m}$ = 120 kg

radius= r = 1.8 m

initial angular velocity = $w_{i} = 1.2 \pi$rad/s

mass of the child = $m_{c}$ = 21kg

By law of conservation of angular momentum,

$L_{i}=L_{f}\\\\I_{m}w_{i}=I_{m+c} w_{f}\\\\w _{f} =\frac{I_{m}w_{i}}{I_{m+c}}$

Here, substitute  $I = \frac{mr^{2} }{2}$

$w _{f} =\frac{I_{m}w_{i}}{I_{m+c}}\\\\w _{f} =\frac{\frac{m_{m}{r _{m}}^{2}}{2} w_{i}}{\frac{m_{m}{r _{m}}^{2}}{2}+{m_{c}r_{c}}^{2} }\\\\w _{f}= \frac{\frac{120(1.8)^{2} }{2} *1.2\pi}{\frac{120(1.8)^{2} }{2} +21(1.8)^{2}}\\\\w _{f} = 2.8 rad/s$

The value of the final angular velocity = 2.8 rad/s

                                                                =2.8/2 π

                                                                = 0.44rev/s

What is angular velocity?

• The rotation rate, which refers to how quickly an object rotates or revolves in relation to another point, is measured vectorially using angular velocity.

• The speed at which an object rotates or revolves around an axis is known as its angular velocity.

• Because a point on a rotating object constantly changes direction, it is challenging to determine the direction of the angular velocity.

• The rotating object only has a fixed direction at its axis.

To learn more about angular velocity, refer:

https://brainly.com/question/20432894

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