Merry go round with a moment of inertia

In summary, the question asks for a step-by-step solution to finding the final angular velocity of a merry go round with a moment of inertia of 1000 kg m^2 when an 80-kg man steps onto the rim, 2m from the axis of rotation. The solution involves using the conservation of angular momentum and finding the moment of inertia for the "merry-go-round + man" system.
  • #1

phy21050

Would someone work through a step by step solution...Thank you. A merry go round with a moment of inertia of 1000kgm^2 is coasting at 2,20 rad/s. When a 80-kg man steps onto the rim, a distance of 2m from the axisof rotation the angular velocity decreases to ? rad/s
 
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  • #2
Originally posted by phy21050
Would someone work through a step by step solution...Thank you. A merry go round with a moment of inertia of 1000 kg m^2 is coasting at 2,20 rad/s. When a 80-kg man steps onto the rim, a distance of 2m from the axis of rotation the angular velocity decreases to ? rad/s

You know that the total angular momentum is constant correct? Well write it out.

Write an expression for the total angular momentum of the merry go round before the man stepped on it. After the man steps on it then once more write an expression for total angular momentum. Then solve for the final angular momentum.

Hint - you're going to need to fine the moment of inertia for the "merry-go-round + man" system.

Give it a try and then we'll go from where you get confused - post the equations that you go to up until you get stuck. Good luck!

Pete
 

1. What is the moment of inertia of a merry go round?

The moment of inertia of a merry go round refers to the resistance it has to changes in its rotational motion. It is determined by the mass and distribution of the objects on the merry go round and the distance of those objects from the axis of rotation.

2. How does the moment of inertia affect the movement of a merry go round?

The moment of inertia affects the speed and acceleration of a merry go round. Objects with a larger moment of inertia will require more force to achieve the same rotational speed as objects with a smaller moment of inertia.

3. What factors affect the moment of inertia of a merry go round?

The moment of inertia of a merry go round is affected by the mass and distribution of objects on the merry go round, as well as the distance of those objects from the center of rotation. The shape and size of the merry go round can also affect the moment of inertia.

4. How does the moment of inertia change if objects are added or removed from a merry go round?

If objects are added or removed from a merry go round, the moment of inertia will change. Adding objects with a larger mass or farther distance from the center of rotation will increase the moment of inertia, while removing objects will decrease it.

5. How is the moment of inertia calculated for a merry go round?

The moment of inertia for a merry go round can be calculated using the formula I = mr², where I is the moment of inertia, m is the mass of the object, and r is the distance from the center of rotation. This formula can be applied for each object on the merry go round and then summed to find the total moment of inertia.

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