Angular Acceleration of a Flywheel Lab

[Shelby8]

Homework Statement

Assume no friction for 1 - 6
1. Draw a free body diagram of the fly wheel (from above), and a free body diagram of the weight (from side).

2. What force appears in both diagrams?

3. What is the relationship between the torque on the flywheel and the tension in the string?

4. What is the relationship between the angular acceleration of the flywheel and the linear acceleration of the weight?

5. What is the formula for the moment of inertia of a solid disk?

6. Based on 1 - 5, write an equation that predicts angular acceleration of the flywheel, given mass and radius and g.

7. Suppose there is friction between fly wheel and stand that holds the fly wheel, so eventually it stops. As the weight drops, will the angular acceleration of the fly wheel be larger than, smaller than, that predicted by the equation in 6?

Homework Equations

angular acceleration = change in angular velocity / change in time
angular momentum = moment of inertia X angular velocity
lever arm = r X sin(theta) (perpendicular distance between axis of rotation and line of action of force) See image
moment of inertia = m X r^2
torque = r X F X sin(theta)[/B]

The Attempt at a Solution

1. See image

2. Tension

3. Torque = radius X Tension (because tension is the force)

4. distance from rest (d) = 1/2 a t^2 --> a = 2 x d / t^2
Not sure how to relate this to angular acceleration?

5. I = M x R^2 / 2

6. Can't answer without #4..

7. Same as 6

 

[CWatters]

Check your FBD of the flywheel from above. Which way does gravity act?

I don't see your FBD for the weight.

 

[haruspex]

For 4, we can take it in stages. First, if the wheel turns through an angke $\theta$, how far does the weight move?
Next, if the wheel rotates at a rate $\dot \theta$, how fast does the weight move? Finally, Q4.

 

[Shelby8]

The mg should act down while the T acts toward the side, I see how I drew that wrong. Am I missing other forces for the flywheel though?

If the wheel turns with theta, like if it turns one rotation (2 pi) then the weight moves the same distance as the circumference of the flywheel? (2 pi r)?
Would the speed be the relation between angular acceleration and linear acceleration? Because F net of the weight = T - mg = m (linear a), and a = α * r.
Is that how to relate them?

so a = (T - mg) / m = α * r ?

 

[Shelby8]

Check your FBD of the flywheel from above. Which way does gravity act?

I don't see your FBD for the weight.

 

[haruspex]

so a = (T - mg) / m = αr

Yes, except which way are you taking as positive for the acceleration? Will T be more or less than mg?

 

[Shelby8]

Yes, except which way are you taking as positive for the acceleration? Will T be more or less than mg?

Oh the weight is moving down so the down is positive. So rewrite it like: a = (mg - T) / m = αr

 

[haruspex]

Oh the weight is moving down so the down is positive. So rewrite it like: a = (mg - T) / m = αr

Ok. Can you attempt 6 now?