Plug in time to find the acceleration

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The discussion focuses on calculating acceleration using time in a rotational motion problem. The initial acceleration of 100 mm/s² was determined using the tangential acceleration formula, but the correct formula for tangential acceleration is a_t = rα. The user successfully calculated angular speed at time = 0 and found that the same calculations apply for subsequent times. They confirmed the calculations for time = 2, resulting in a_t = 100 mm/s² and a_n = 50 mm/s². Ultimately, the total acceleration was calculated as A = 111.8 mm/s².
Jason03
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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
 
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Jason03 said:
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?
 
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...
 
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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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