Moment of Inertia and Angular Speed

In summary, the conversation discusses the concept of work and energy in relation to a top with a moment of inertia of 4.40 10-4 kgm2 and a constant tension of 5.19 N. The question asks for the angular speed of the top after 80.0 cm of string has been pulled off the peg, assuming the string does not slip. The hint leads to the use of the equation delta K = .5I(final angular velocity^2 - initial angular velocity^2) to solve the problem.
  • #1
TrippingBilly
27
0
A top has a moment of inertia of 4.40 10-4 kgm2 and is initially at rest. It is free to rotate about the stationary axis AA'. A string, wrapped around a peg along the axis of the top, is pulled in such a manner as to maintain a constant tension of 5.19 N. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after 80.0 cm of string has been pulled off the peg? (The picture of the top shows it rotating clockwise about a vertical axis A)

This question has me stumped. If someone could point me in the right direction with regards to a concept I need to know or something I would appreciate it.
 
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  • #2
Hint: How much work is done by the string?
 
  • #3
At first I didn't see where you were going, but then I realized that work = change in energy. Which enabled me to use that wonderful equation
delta K = .5I(final angular velocity^2 - initial angular velocity^2). Thanks for the hint!
 

FAQ: Moment of Inertia and Angular Speed

1. What is the moment of inertia?

The moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is dependent on the mass, shape, and distribution of mass of the object.

2. How is the moment of inertia calculated?

The moment of inertia is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. The formula is I = mr², where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

3. What is angular speed?

Angular speed is a measure of how quickly an object is rotating. It is defined as the change in angular displacement over a period of time and is typically measured in radians per second.

4. How is angular speed related to moment of inertia?

The angular speed of an object is inversely proportional to its moment of inertia. This means that as the moment of inertia increases, the angular speed decreases, and vice versa.

5. What factors affect the moment of inertia?

The moment of inertia is affected by the mass, shape, and distribution of mass of an object. Generally, objects with more mass, a greater distance from the axis of rotation, and a more spread-out distribution of mass will have a larger moment of inertia.

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