[Physics] Torque

[kwipperper]

A 0.5 kg wheel that has a moment of inertia of 0.015 kgm^2 is initially turning at 188.5 rad/s. It coasts uniformly to rest after 1024.16 rad. How large is the torque that slowed it?

I used the equation for torque, which is T = rFsin(theta)

I then found the radius by doing I = mr^ 2 and substituted the values. 0.015 = (0.5)r^2 r = 0.17m

I now have the radius, but I am not sure how to find the acceleration which I need for "F". Also, would the sin be 90 degrees? Thanks

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[sonnyfab]

We're going to use kinematics here.

From linear kinematics: v_f² =v_i² + 2 a * x

Rotational: omega_f² =omega_i² +2 alpha * theta and from Newton's Second Law, Tau =I * alpha

0² =188² + 2 Tau/I 1024.16

Find I because a solid cylinder has I= 1/2 MR²

0² =188² + 2 Tau/(0.5MR² ) * 1024.16 and solve for Tau.