they are just asking for alpha at t=3 s, which is 420 rad/s^2. I am fairly sure of this because it is the answer in the back of the book... However, i am struggling to figure out omega at t=3 s which should be 500 rad/s but i need the work to back it up and I'm not sure which equations to use.
i thought it was
W = delta K = 1/2(I)(omega final)^2 - 1/2(I)(omega initial)^2...?
or do i use the formula
W= (integral from theta initial to theta final) torque d-theta?
so is the geometric relationship that when alpha increases, so does omega? do i need to use an integral?
dw= (integral)alpha dt? but how can i differentiate this if there are no variables?
i come up with dw=alpha*t + c but when i plug in t=3, i still get 1260...
Homework Statement
A 32.0 kg wheel, essentially a thin hoop with r=1.20 m is rotating at 280 rev/min. It must be brought to stop in 15.0 s. How much work must be done to stop it?
Homework Equations/The Attempt at a Solution
I=mr^2=46.08 kg*m^2
W=(1/2)I\omegaf^2 - (1/2)I\omegai^2...
Homework Statement
A pulley, with a rotational inertia of 1.0 x 10^-3 kg*m^2 about its axle and a radius of 10 cm, is acted on tangentially at its rim. the force magnitude varies in time as F=0.50t + 0.30t^2, with F in Newtons and t in seconds. The pulley is initially at rest . At t=3.0 s...