To find torque (which we write as $\tau$), we use this formula:

$\tau = r \cdot F \cdot \sin(\theta)$

Let’s break down what each part means:

• $\tau$: This is the torque, measured in newton-meters (N·m).
• $r$: This is the length of the lever arm, measured in meters (m).
• $F$: This is the force applied, measured in newtons (N).
• $\theta$: This is the angle between the force direction and the lever arm, which can be in degrees or radians.

How Lever Arm Length Affects Torque

1. Making $r$ Larger:

   • If you increase the length of the lever arm ($r$), the torque ($\tau$) increases too.
   • For example, if you double the lever arm length, you double the torque.

2. Changes in Force:

   • If the force ($F$) stays the same, a longer lever arm gives you more torque:
     • For example, if $F = 10 \, \text{N}$:
       • If $r = 0.5 \, \text{m}$, then $\tau = 5 \, \text{N·m}$
       • If $r = 1.0 \, \text{m}$, then $\tau = 10 \, \text{N·m}$

3. The Role of Angle:

   • When the angle ($\theta$) is $90^\circ$, the torque is at its highest because $\sin(90^\circ) = 1$.
   • If the angle is $0^\circ$ or $180^\circ$, then the torque ($\tau$) is $0$.

To Sum It Up

Torque is increased when you have a longer lever arm and when you have the right angle. This shows how important lever arms are in understanding how things rotate.