a rotating wheel requires 8 seconds to rotate 31.2 rev..Its angular speed at the end of the 8s is 50 rad/s....

Question

FIND...
a. the constant acceleration fo the wheel..
b. the initial angualr velocity of the wheel...

so i tryed doing it myself and got 6.37rad/s^2 for a .....& -.98rad/s for b....am i right??

Answer 1

Well for the 31.2 revolutions, the average speed is (31.2revsx2 pi rad/rev) / 8s = 24.5rad/sec
since the final speed is higher than the average the wheel is accelerating.
Assuming constant accel (from the question) the wheel accelerated from the average speed at the mid point in time to the final speed. In other words
acceleration = (final speed - average speed) / 4 secs
= (50-24.5)/4 = 6.375rad/s^2

From constant acceleration the speed increased in 8 secs was Acceleration x 8 secs.
Vinit = Vfin-(8 x A)
= 50 - (8 x 6.375) = 50-51 = -1rad/s

So yes, you're right.

Answer 2

You can always check your answer yourself by plugging your numbers back into one of the equations:

e.g. theta = w0*t + 1/2*alpha*t^2

When you do this you will find that your solution does not work.


You are given theta, w, and t. Solving this will require you use two angular kinematic equations.

For example use:
w = w0 + alpha*t

re-arrange to get w0 = w-alpha*t, and substitute into:

theta = w0*t + 1/2*alpha*t^2

getting

theta = (w-alpha*t)*t + 1/2*alpha*t^2
theta = w*t - 1/2*alpha*t^2

now you have one only one unknown, alpha, in your equation. Solve this to find part (a)

Then replug into your newly found alpha into the equation of your choice, probably

w = w0 + alpha* t

and solve for w0.