## Torque and Angular Acceleration

**Learning Goal: **To understand and apply the formula **τ** =*I*ɑ to rigid objects rotating about a fixed axis.

To find the acceleration ɑ of a particle of mass m, we use Newton’s second law: , where is the net force acting on the particle.

To find the angular acceleration ɑ of a rigid object rotating about a fixed axis, we can use a similar formula: **τ _{net} = Iɑ**, where

**τ**Σ

_{net}=**τ**is the

*net torque*acting on the object and

*I*is its moment of inertia.

In this problem, you will practice applying this formula to several situations involving angular acceleration. In all of these situations, two objects of masses m_{1} and m_{2} are attached to a seesaw. The seesaw is made of a bar that has length *l* and is pivoted so that it is free to rotate in the vertical plane without friction.Assume that the pivot is attached tot he center of the bar.

You are to find the angular acceleration of the seesaw when it is set in motion from the horizontal position. In all cases, assume that m_{1>}m_{2.}

**A) Assume that the mass of the swing bar, as shown in the figure, is negligible. **

**B) In what direction will the seesaw rotate, and what will the sign of the angular acceleration be?**

**C) Now consider a similar situation, except that now the swing bar itself has mass m _{bar}.**

**D) In what direction will the seesaw rotate and what will the sign of the angular acceleration be?**

## Answer ( 1 )

A) Assume that the mass of the swing bar, as shown in the figure, is negligible.

Find the magnitude of the angular acceleration ɑ of the seesaw.

=>

α =

B) In what direction will the seesaw rotate, and what will the sign of the angular acceleration be?

=> The rotation is in the counterclockwise direction and the angular acceleration is positive.

C) Now consider a similar situation, except that now the swing bar itself has mass mbar.

Find the magnitude of the angular acceleration α of the seesaw.

=>

α=

D) In what direction will the seesaw rotate and what will the sign of the angular acceleration be?

=> The rotation is in the counterclockwise direction and the angular acceleration is positive.