Moment of inertia and angular acceleration

[physicssss]

Homework Statement

If the fall height of the mass is doubled, the angular acceleration of the wheel will
a. decrease by an unkown amount
b. remain unchanged
c. decrease by a factor of 2
d. increase by an unknown amount
e. increase by a factor of 2

Homework Equations

The Attempt at a Solution

well since angular acceleration is slope of linear graph and if we double the height(x-axis) I think the angular frequency will remain constant. But maybe I'm wrong. That is why I need help.

 

[Simon Bridge]

If the fall height of the mass is doubled, the angular acceleration of the wheel will

The description is not complete.
Fall of what and how is this related to a wheel?

Is this a mass falls onto a wheel, where it stays somehow, and so makes it turn?
Hint: conservation of energy.

 

[physicssss]

its a suspended mass attached to to the hub of a bicycle wheel through a pulley. so basically we release the wheel (which is attached to a table) and it turns from the weight of the suspended mass until the mass reaches the floor.
Anyways I have come to a new conclusion that the angular acceleration doubles from the height being double.
I still need confirmation though.

 

[Simon Bridge]

Yeh - the final speed is higher, but the time is also longer.
You need to use the kinematic equations for rotating bodies or conservation of energy if you want a mathematical approach - or you can use your understanding of gravity.

If the mass were free to just fall - not attached to the wheel - how would the acceleration be affected by the distance it has to fall?

 

[Nickie]

I would approach this question by first looking at the equations and principles involved. The moment of inertia of a rotating object is directly proportional to its mass and the square of its distance from the axis of rotation. This means that if the fall height of the mass is doubled, the moment of inertia of the wheel will also double.

Now, looking at the equation for angular acceleration, we can see that it is inversely proportional to the moment of inertia. This means that as the moment of inertia increases, the angular acceleration decreases. Therefore, if the fall height is doubled and the moment of inertia is doubled, the angular acceleration will decrease by a factor of 2 (option c).

However, it is important to note that this assumes all other variables, such as the force causing the fall and the friction in the system, remain constant. In reality, these factors may also affect the angular acceleration, so it may not be a perfect 2:1 decrease. Further experimentation or calculations may be needed to determine the exact change in angular acceleration.