A uniform disk of mass M = 3 kg and radius r = .22 meters is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1 n * m
What is the time required for the disk to reach an angular speed of 800 rpm
tor = i a
i = rotational intertia
a = acc
The Attempt at a Solution
So I convert 800 rotations / min to 80/6 rotations a second.
since angular acceleration = Torque / rotational interta, and I have torque is 1 n * m and rotational intertia = (1/2) m r^2
so I have (1) / (1/2)(3)(.22)^2 = 13.77
so that should be my angular acceleration right?
Now to find time all I have to do is use euqation
[itex] W_0 + ax t = W_x [/itex]
w_o = 0 so
t = (W_x)/(a_x)
t = 80/(6)(13.77) = .9682 s
but my books answer was 6.08 seconds.
Does anyone know where I went wrong? I have a feeling I calculated acceleration wrong :/