# Math Help - Angular retardation

1. ## Angular retardation

I'm really struggling with a engineering science question about finding angular retardation. The question is -

a rotating system has a mass of 160kg and at all speeds the frictional resistance is equivalent to a torque of o.9Nm.

During a test the speed was increased from 160rpm to 220rpm in 4 seconds by a applied torque of 10.7 Nm.

If the system is rotating at 220 rpm and the driving torque is eliminated find the angular retardation.

I guess it has something to do with the frictional resistance but I don't know how to incorporate it, all other work I have done I've used a time of retardation and the speeds to figure it out but in this question I have no time.

Thanks guys

2. ## Re: Angular retardation

You'll need to use kinetic equations here (as opposed to the questions you solved previously were you could use kinematic equations).

Start with the torque balance equation (i.e. the angular equivalent of Newton's 2nd law):
$\sum M=I\alpha$
in which $\sum M$ is resultant torque, $I$ is mass moment of inertia, and $\alpha$ is angular acceleration/retardation.

$\alpha$ is the variable that you want to solve this equation for. $\sum M$ is known, but you still need to find the value of $I$.

To find $I$ apply the angular momentum equation to the test data that was given:
$M\Delta t = I \omega_2 - I \omega_1$