# Angular Velocity Problem - Merry Go Round

• vm310
In summary, the merry go round's total moment of inertia has increased by 1950 kg because of the addition of the individual moment of inertia of the kids jumping on.
vm310
A 4.8m diameter merry-go-round is rotating freely with an angular velocity of 0.8rad/s. Its total moment of inertia is 1950(kg)(m2). Skid, Mitch, Larry, and Greezy all jump on at the same time. They each have a mass of 65kg.What is the angular velocity now?

Relevant equations
$$\omega=\frac{v}{r}$$

$$I=\frac{1}{2}$$mv2

## The Attempt at a Solution

I'm totally lost. Someone please give me a hint

Thanks

vm310 said:
$$I=\frac{1}{2}$$mv2

This is not actually correct. 1/2 mv^2 is the formula for kinetic energy. The moment of inertia of a rotating body is something totally different, and it depends on both the mass of the body and its shape. But you don't have to worry about how to calculate it, because the problem *gives* you its numerical value right from the start.
vm310 said:
I'm totally lost. Someone please give me a hint

There is a relationship between moment of inertia, angular velocity, and angular momentum. If you look at it closely, it should become clear what to do.

EDIT: Hint 1 - One of these three quantities changes after the kids jump on, as compared to before, which results in a change in another one of the quantities.

Hint 2 - As is often the case in physics, a general conservation law is what allows us to understand how the system will respond after the change has occurred.

Thank you for the quick response. I know that,

$$L=I\omega$$

and that,

$$L=mvr$$

I know I'm supposed to sum the masses of everyone who jumps on, but am I suppose to sum the radius also?

vm310 said:
Thank you for the quick response. I know that,

$$L=I\omega$$

Right, and the quantity that changes (before vs. after) is the moment of inertia of the merry go round, because now it has the additional individual moments of inertia of the people standing on it. If you can figure out by how much I changes, you can figure out how much omega changes (because angular momentum is conserved).

Thanks cepheid I got it!

## 1. What is angular velocity?

Angular velocity is the measure of how fast an object is rotating or turning. It is typically measured in radians per second or degrees per second.

## 2. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related through the equation v = rω, where v is linear velocity, r is the distance from the center of rotation, and ω is angular velocity. As angular velocity increases, linear velocity also increases.

## 3. How does angular velocity change on a merry go round?

On a merry go round, the angular velocity remains constant as long as there is no external force acting on it. This means that the speed of rotation will not change unless there is a force that causes it to speed up or slow down.

## 4. How does the radius affect angular velocity on a merry go round?

The radius does not directly affect the angular velocity on a merry go round. However, as the radius increases, the linear velocity also increases, as seen in the equation v = rω. This means that objects located farther from the center of rotation will have a higher linear velocity than objects closer to the center.

## 5. What is the difference between angular velocity and tangential velocity?

Angular velocity is a measure of how fast an object is rotating, while tangential velocity is a measure of how fast an object is moving along a circular path. Tangential velocity is related to angular velocity through the equation v = rω, where v is tangential velocity, r is the distance from the center of rotation, and ω is angular velocity.

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