Understanding Torque
Torque (\(\tau\)) is a measure of the rotational force applied to an object around a pivot point. The formula for torque is given by:
\[ \tau = F \cdot r \cdot \sin(\theta) \]
- \(\tau\): Torque (Nm)
- \(F\): Force applied (N)
- \(r\): Distance from the pivot (m)
- \(\theta\): Angle between the force vector and the lever arm (degrees)
Example Calculations
Example 1:
If \(F = 50N\), \(r = 0.5m\), and \(\theta = 30^\circ\):
\[
\tau = 50 \cdot 0.5 \cdot \sin(30^\circ) = 12.5 \, \text{Nm}
\]
Example 2:
If \(F = 100N\), \(r = 2m\), and \(\theta = 45^\circ\):
\[
\tau = 100 \cdot 2 \cdot \sin(45^\circ) \approx 141.42 \, \text{Nm}
\]