Physics overview
What is rotational work?
Rotational work is the energy transferred when torque turns an object through an angular displacement.
Formula
Rotational work formula
Rotational WorkW = τθ
- W is rotational work in joules.
- τ is torque in N·m.
- θ is angular displacement in radians.
Worked example
A torque of 8 N·m rotates an object through 3 radians
- Write the formula: W = τθ.
- Substitute the values: W = 8 × 3.
- Calculate rotational work: W = 24 J.
Rearranged equations
Solve for torque or angular displacement
Torque
τ = W ÷ θ
Divide rotational work by angular displacement.
Angular displacement
θ = W ÷ τ
Divide rotational work by torque.
Physical relationship
Torque and angle both affect work
Rotational work increases when torque increases, angular displacement increases, or both increase.
Units
Standard SI units
Use joules for rotational work, newton meters for torque, and radians for angular displacement.
Real-world applications
Where rotational work is used
- Motors and rotating machinery.
- Wheels, gears, and flywheels.
- Turbines and mechanical shafts.
- Vehicle drivetrain systems.
- Robotics and rotational actuators.
Calculation limits
Important assumptions
- All entered values must be greater than zero.
- Torque is treated as constant.
- Angular displacement must be entered in radians.
- Vector direction is not represented.
- Units are not converted automatically.
Related tools
Continue your rotational analysis
Use the Torque Calculator to calculate torque, force, or lever arm distance.
Use the Rotational Power Calculator to calculate power, torque, or angular velocity.
Questions and answers
Rotational work calculator FAQ
What formula does the rotational work calculator use?
It uses W = τθ, where rotational work equals torque multiplied by angular displacement in radians.
What is rotational work?
Rotational work is the energy transferred when a torque rotates an object through an angular displacement.
How do you calculate torque from rotational work?
Divide rotational work by angular displacement using τ = W ÷ θ.
What units are used for rotational work?
Rotational work is measured in joules, torque in newton meters, and angular displacement in radians.