A wheel has a coonstant rotational acceleration of 3.0 rad/s^2. During a certain 4.0 s interval, it turns through an angle of 120 rad. Assuming that the wheel starts from rest, how long is it in motion at the start of the 4s interval.
I just need help in getting started. I know that the 3.0 rad/s^2 is the alpha roational acceleration and 120 rad is the theta. I do not have though rotational velocity.
Thank you
The way you ask the question does not make sense. At the START of the 4s interval, it is at rest, and you are asking "how long is it in motion?" At the start of the interval, it has not been in motion at all. You have already told us how long it is in motion, so why are you asking "how long"?
Perhaps you meant to ask how large an angle it turns through AT THE END OF 4 seconds. In that case,
Total angle of rotation = (1/2)*alpha* t^2
The displacement from t=0 is not 120, but 120 plus the displacement starting at the four second period
totaldisplacement=initialdisplacement + initalangularspeed*time + 1/2 angular acceleration*time^2
Starting from rest...
120+ initialdisplacement= +0+ 1/2*3 (t )^2
solve for t. this is the time from starting to the end of the four second period.
Now, initial displacement is 1/2*3(t-4)^2
so
120+1/2*3(t-4)^2=1/2*3 (t )^2
solve for t. You are looking for t-4 in this problem.
check my thinking.
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