# Meri go round: Angular momentum

• kalupahana
In summary, the moment of inertia of the merry-go-round after 4 men with a mass of 65 kg each enter at the edge is 12265 kg m2. By applying the conservation of angular momentum, the final angular velocity is calculated to be 1.099 rad/s. However, this is incorrect as the shape of the ride cannot be assumed to be a point particle. The correct answer is 0.004 rad/s.
kalupahana

## Homework Statement

A meri go round is rotating it vertical axis through center with a diameter 4.5m. It's moment of inertia is 1750 kg m2 and angular velocity is 0.70 rad/s. 4 men with mass 65 kg instantly enter the the edge of the meri go round. Calculate the angular velocity of meri go round after that instant.

## Homework Equations

Conservation of angular momentum
I1ω1 = I2ω2

I = ma2

## The Attempt at a Solution

I1 = 1750 kg m2

The mass of meri go round
1750 = ma2
1750 = m(4.5/2)2
(1750 x 4)/ (4.5)2 = m

The mass of meri go round after 4 men get in

m = (1750 x 4)/ (4.5)2 + 65 x 4
m = [7000 + (260 x (4.5)2]/(4.5)2
m = 12265/(4.5)2

Then
I2 = 12265 kg m2

Applying conservation of angular momentum

1750 x 0.70 = 12265 ω2

The mistake you've made is 'I=ma^2' which is only valid for a point particle.
The ride could be any complex shape you can't say anything about.

So moment of inertia after 4 men go on is: 1750 + 4*(65)*((4.5/2)^2)

the men are assumed to be point masses at a distance a/2 so their moments of inertia is m(a/2)^2 each.
This can be just added to the moment of inertia of the ride, as the axis of rotation stays same throughout the problem.

## 1. What is angular momentum?

Angular momentum is a property of a rotating object that describes its tendency to continue rotating. It is a vector quantity that depends on the mass, shape, and speed of the object.

## 2. How is angular momentum calculated?

Angular momentum is calculated by multiplying the moment of inertia (a measure of an object's resistance to rotation) by the angular velocity (the rate of change of the object's angular position).

## 3. What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system remains constant as long as there are no external torques acting on the system. This means that if one part of a system gains angular momentum, another part must lose an equal amount.

## 4. How does angular momentum relate to rotational motion?

Angular momentum is directly related to rotational motion. In fact, it is considered the rotational equivalent of linear momentum. Just as an object with linear momentum will continue moving in a straight line unless acted upon by a force, an object with angular momentum will continue rotating unless acted upon by a torque.

## 5. How is angular momentum used in real-world applications?

Angular momentum has many practical applications in physics and engineering. It is used in the design of vehicles such as rockets and satellites, in the study of celestial bodies and their orbits, and in the development of gyroscopes and other rotating devices.

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