Finding moment of inertia for problem 8

[jimbo71]

Homework Statement

see problem 8 attachment

Homework Equations

see problem 8 attempt attachment

The Attempt at a Solution

see problem 8 attempt attachment
I think I have solved the problem correctly and through my method I determine the moment of inertia to be 4.3 kg*m^2. However I'm not sure if the equations I used to find velocity and acceleration are valid in this situation.

 

[alphysicist]

Hi jimbo71,

Homework Statement

see problem 8 attachment

Homework Equations

see problem 8 attempt attachment

The Attempt at a Solution

see problem 8 attempt attachment
I think I have solved the problem correctly and through my method I determine the moment of inertia to be 4.3 kg*m^2. However I'm not sure if the equations I used to find velocity and acceleration are valid in this situation.

I think the assumption you have made (that is not necessarily true) is that the wheel is a uniform disk.

Once you found the linear acceleration of 0.75 m/s², you can directly find the angular acceleration alpha from $a=r\alpha$.

Then you can use the torque equation like you did, but there is no need try to write out an expression for I, since I is what you want. Just use:

$$\tau = I\alpha$$

and solve for I.