Moment of inertia, when a velocity of ball triples?

In summary, the moment of inertia remains the same when the velocity of a ball triples because it only depends on the mass and radius, according to the formula for moment of inertia of a solid sphere. At relativistic speeds, there may be a mass dilation effect, but this was not discussed in the conversation.
  • #1
rcmango
234
0

Homework Statement



What happens to the moment of inertia when the velocity of a ball triples?


Homework Equations





The Attempt at a Solution



does the moment of inertia triple? become nin times bigger, remain the same, or become only 1/3 of what it was?

not sure, what is really going on with the inertia in this situation.
help please.
 
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  • #2
The first question I would ask myself is:

What does the moment of inertia depend upon? Does it depend on the velocity?

Do you know what moment of inertia is and how it is defined? Do you know the formula for the moment of inertia of a solid sphere (or how to calculate it)? If so, you should be able to answer this question yourself.
 
  • #3
okay, so i assumed that the inertia will stay the same because the radius and the mass are in the formula only.
 
  • #4
rcmango said:
okay, so i assumed that the inertia will stay the same because the radius and the mass are in the formula only.

you are correct , though i think at relativistic speeds you get a mass dilation but i don't know jack about that
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion, but for rotational motion.

2. How is moment of inertia calculated?

The moment of inertia depends on the shape and mass distribution of the object. It can be calculated using the object's mass, distance from the axis of rotation, and the object's inertia tensor.

3. How does the velocity of a ball affect its moment of inertia?

The velocity of a ball does not directly affect its moment of inertia. However, an increase in velocity would result in an increase in the ball's kinetic energy, which would in turn affect its moment of inertia.

4. Can the moment of inertia change?

Yes, the moment of inertia can change if there is a change in the mass distribution or the axis of rotation of the object. It can also be affected by external forces such as torque.

5. How does tripling the velocity of a ball affect its moment of inertia?

If the mass and shape of the ball remain constant, tripling the velocity would result in a nine-fold increase in the ball's kinetic energy. This would also result in a change in its moment of inertia, making it more difficult to change the ball's rotational motion.

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