Work Done by Torque Calculator

Torque (t in Nm):



Angular Displacement (θ in radians):



Calculate

Work Done by Torque (Wt in Joules):

The work done by torque is a concept in physics that describes the energy transferred when a force causes a rotational displacement. This calculation is essential in various mechanical and engineering applications, such as the movement of gears, motors, or any rotating objects. Understanding how torque results in work done helps professionals design systems that efficiently utilize energy.

Formula
The formula to calculate the work done by torque is:

Work Done by Torque (Wt) = Torque (t) × Angular Displacement (θ)

Where:

• Wt is the Work Done by Torque, measured in Joules (J).
• t is the Torque, measured in Newton-meters (Nm).
• θ is the Angular Displacement, measured in radians.

How to Use

1. Input the Torque (t) applied in Newton-meters.
2. Enter the Angular Displacement (θ) in radians.
3. Click the “Calculate” button to find out the Work Done by Torque (Wt).

Example
If you apply a torque of 10 Nm over an angular displacement of 2 radians, the work done by torque is calculated as follows:

Wt = 10 × 2 = 20 Joules

This means that 20 Joules of energy are transferred during this rotational motion.

FAQs

1. What is torque?
   Torque is a measure of the force causing an object to rotate about an axis. It is often referred to as the rotational equivalent of linear force.
2. What is angular displacement?
   Angular displacement is the angle through which an object rotates or moves on a circular path, measured in radians.
3. What units are used to calculate work done by torque?
   Torque is measured in Newton-meters (Nm), angular displacement in radians, and work done by torque in Joules (J).
4. Why is torque important in rotational motion?
   Torque determines how much rotational force is applied to an object, which is essential in systems like motors, engines, and mechanical levers.
5. Can I calculate work done by torque in degrees?
   The standard unit for angular displacement is radians. If using degrees, convert them to radians by multiplying by π/180 before using the formula.
6. How do you measure angular displacement?
   Angular displacement is often measured using a protractor or through mathematical calculations in physics experiments.
7. What is the difference between force and torque?
   Force is a linear push or pull, while torque is a rotational force that causes an object to rotate around a point or axis.
8. What happens if there is no angular displacement?
   If angular displacement (θ) is zero, the work done by torque will also be zero since no rotational movement occurred.
9. Can torque exist without causing work?
   Yes, if the object does not rotate, no work is done by the torque, even if the force is applied.
10. What is the relationship between torque and work?
    Work done by torque is directly proportional to both the applied torque and the angular displacement of the object.
11. How is torque different from energy?
    Torque is a measure of rotational force, while energy is the ability to do work, which includes the work done by torque.
12. What is the physical significance of work done by torque?
    It represents the amount of energy transferred to rotate an object, essential in understanding power and efficiency in mechanical systems.
13. What are some practical applications of work done by torque?
    Applications include the design of engines, turbines, windmills, and any system involving rotational forces.
14. What happens if the torque is applied over a longer angular displacement?
    The longer the angular displacement over which torque is applied, the more work is done, resulting in more energy transferred.
15. Can negative work be done by torque?
    Yes, negative work occurs if the force opposes the direction of motion, which can happen in braking or resisting systems.
16. What role does torque play in electrical motors?
    Torque is crucial in electrical motors, as it directly relates to the motor’s ability to rotate shafts and drive mechanical systems.
17. Does the calculator work for both clockwise and counterclockwise rotations?
    Yes, the calculator works for both, but the sign of torque may differ depending on the direction of the rotation.
18. Is work done by torque affected by the speed of rotation?
    No, the speed of rotation does not directly affect the work done by torque, but it influences other factors like power and efficiency.
19. What happens if torque is applied but no angular displacement occurs?
    If no angular displacement occurs, no work is done, even if torque is applied.
20. Can this formula be used for non-uniform motion?
    The formula assumes uniform angular displacement. For non-uniform motion, more complex calculations may be needed.

Conclusion
The work done by torque calculator provides a simple way to calculate the energy transferred in rotational systems. By entering the torque applied and the angular displacement, you can determine how much work is done in moving an object along its circular path. This tool is invaluable for mechanical and engineering applications where rotational motion plays a key role, helping to ensure the efficient design of machines and structures.