Homework Help: Help! flywheel

1. Apr 25, 2005

masterthephysics

Question:
A flywheel 0.600 m in diameter pivots on a horizontal axis. A rope is wrapped around the outside of the flywheel, and a steady pull of 40.0 N is exerted on the rope. The flywheel starts from rest, and 5.00 m of rope are unwound in 2.00 s.

Okay i have tried finding the angular velocity by first finding the linear velocity=5/2 then putting it into v=omega*r and making omega the subject. Then after finding omega I substituted it into the equation of (omega - 0)/2 but its wrong :(

Where have I gone wrong? Can someone help me out? thanks in advance

2. Apr 25, 2005

OlderDan

You have not actually stated the question you are trying to answer. Something about acceleration I bet. In any case, you have probably confused average velocity with final velocity. The information given in the problem gives you the average velocity. From that you have to decuce final velocity and probably use that to find acceleration.

3. Apr 25, 2005

masterthephysics

What is the angular acceleration of the flywheel?

4. Apr 25, 2005

OlderDan

5. Apr 25, 2005

masterthephysics

i got 4.17 as angular accerleration but it was wrong

6. Apr 25, 2005

whozum

Acceleration = Velocity / Time.. you found the velocity, you have the time..

7. Apr 25, 2005

masterthephysics

would that give me the tangential acceleration?
the i can work out a_tan = r*alpha?
alpha = angular acceleration

8. Apr 25, 2005

whozum

Alternatively if oyu can find the angle swept during the 2s, you can find the acceleration using the relationship

$$\theta = \frac{\alpha t^2}{2}$$

9. Apr 25, 2005

OlderDan

Either you have confused the average and final velocity, or used the given diameter instead of the radius in your calculation.

10. Apr 25, 2005

masterthephysics

so to work out theta i would use s=r*theta with s=5 and r=0.3?

11. Apr 25, 2005

OlderDan

That would be correct for using

$$\theta = \frac{\alpha t^2}{2}$$

You can also do it using your original velocity calculation, but you need to understand that is the average velocity, which is 1/2 the final velocity.

12. Apr 25, 2005

masterthephysics

alright - i tried using the equation above with theta but I still get the wrong answer for the acceleration: i did -
5/0.3 = (alpha(4))/2 and got 8.33

13. Apr 25, 2005

OlderDan

That looks right.. what are they giving as the correct answer?

By velocity it would be average velocity = 5m/2 sec = 2.5m/sec. So omega = v/r = 5m/2sec/.3m = 8.33/sec. The final angular velocity would be twice that and the time to reach that angular velocity is 2 seconds

alpha = 2*8.33/sec/2sec = 8.33/sec^2

Last edited: Apr 25, 2005
14. Apr 25, 2005

masterthephysics

thanks!! i just realised that i did something wrong haha

15. Apr 28, 2005

la673

how would u work out the final kinetic energy here?
i tried using k_e=.5*I*(omega)^2

but I is an unknown, as to find I, u use I=kmr2, so I=(1/2)*m*(.03)^2 (as this is a solid cylinder)
and i hav no idea how to work out m.

wait can u use f=ma? so 40 n = m* a, where a =r*alpha, or=2.499

so 40=m*2.499 and m=16.01kg?

Last edited: Apr 28, 2005
16. Apr 28, 2005

whozum

You would need the mass to find kinetic energy.

17. Apr 28, 2005

OlderDan

If you have found the angular deceleration correctly, you now have everything needed to figure out I, and you need to do it.