Find mom of inertia and frictional torque

[physicsgirl4]

 

[I like Serena]

Welcome to PF, physicsgirl4!

Homework Statement

1. A wheel is initially at rest. An external torque of 60 N m is applied to the wheel for 12 s, giving the wheel an angular velocity of 800 rev/min. The external torque is then removed, and the wheel comes to rest 100 s later. Find the moment of inertia of the wheel and the frictional torque(constant)

Homework Equations

torque = moment of interia (I) . angular velocity

angular velocity = dw/dt

The Attempt at a Solution

angular acceleration = 800.2pi/60.12 = 20/9pi revs/s

That's the right value!

But the wrong unit...
You converted revolutions to radians, and it's an angular acceleration instead of a angular velocity.
The unit should be rad/s².

mom of inertia = 60/(20/9) = 27kgm^2

You seem to have lost a pi here...
But the value is not correct yet anyway, since you haven't taken friction into account yet.

Is this correct ? Then I don't know how to find the frictional torque? I have seen the equation net torque = ext torque + frictional torque ..although from this I don't know how to find net torque?

Let's set up the equations first:

In the first stage:
$$T_{net} = T_{ext} - T_{fric} = I \cdot \alpha_1$$
$$T_{ext} = 60 N m$$
$$\alpha_1 = {800 \cdot 2\pi \over 60 \cdot 12} {rad \over s^2}$$

In the second stage:
$$- T_{fric} = I \cdot \alpha_2$$
$$\alpha_2 = - {800 \cdot 2\pi \over 60 \cdot 100} {rad \over s^2}$$

This is a set of equations, can you solve it?