Question

An object whose moment of inertia is 2.5 kg · m^2 experiences the torque shown in the figure below. What is the object's angular velocity at t = 1.6 s? Assume it starts from rest.

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So far, I know that that to find the acceleration, it's T/I (or 2/2.5) and then I just have to multiply the time to get the angular velocity, but I keep getting the wrong answer. What am I doing wrong?

Answer 1

no
your torque is not constant from 0 to 1 second
it is
Torque = 2 t
for 0 to 1 second
a = 2 t/2.5
v = (2/2.5)(t^2/2) = 1/2.5 rad/s at 1 second
------------------------
NOW that is your constant torque of 2 from 1 second to 2 seconds
initial v = 1/2.5 rad/s
a = dv/dt = 2/2.5
v = 1/2.5 + (2/2.5)1
v = 3/2.5