\[\tau=rF\sin(\theta)\]
Variables
taujoint torque (N·m)
rmoment arm length (m)
Fapplied force (N)
thetaangle between force and lever arm (rad)
Description
What is this formula?
This formula calculates the torque generated around a joint by a force applied at a certain distance and angle from the rotation axis. Torque determines rotational motion in biomechanics.
When to use it
Use this formula in biomechanics, kinesiology, rehabilitation, or sports science when analyzing joint loading and muscular action.
Example
A muscle applies:
F=250 N
At a distance:
r=0.04 m
Angle:
theta=90°
Formula:
tau=r*F*sin(theta)
Substitution:
tau=0.04*250*sin(90°)
Result:
tau=10 N·m
The joint torque produced is 10 N·m.
Applications
- Human movement analysis
- Sports biomechanics
- Prosthetic design
- Rehabilitation engineering
- Muscle mechanics