Moment of Inertia: Problem 8 Homework Solutions

[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.

 

[thomate1]

I would suggest double checking your equations and units to ensure accuracy. Additionally, it may be helpful to provide more context or information about the problem so that others can better understand your approach and provide feedback. Overall, it seems like you have a good understanding of the concept of moment of inertia and how to calculate it, so keep up the good work!