Plug in time to find the acceleration

[Jason03]

Heres the problem I am working on...

http://img502.imageshack.us/img502/1613/rotut5.jpg

Im trying to figure how to plug in time to find the acceleration...

I found the first acceleration of 100mm/s^2...but I am not sure how to get the others...

I was using the formula

$$a_{t} = r\theta$$

$$a_{n} = r\omega^2$$

 

[Doc Al]

I was using the formula

$$a_{t} = r\theta$$

$$a_{n} = r\omega^2$$

That first equation should be:

$$a_{t} = r\alpha$$

How can you find the angular speed at each of those times?

 

[Jason03]

at time = 0 I was able to do

$$a_{t} = r\omega = 9(.200)(.5) = .100 = 100mm/s^2$$

and that is correct for the first answer...

but for the other times I wasnt sure...

 

[Jason03]

ok I figured it out for time at 2...and its the same for each time...its just

$$a_{t} = r\alpha = (.200)(.5) = .100$$

$$\omega = \omega_{o} + \alpha(t)$$

$$\omega = .5 rad/s$$

$$a_{n} = r\omega^2 = (.200)(.5)^2 = .050$$

$$A = \sqrt{a_{t}^2+a_{n}^2} = 111.8 mm/s^2$$