Work Done in 3/4th of Rotation

When a mass moves in a circular path with constant speed, it experiences centripetal force directed towards the center of the circle. This force is responsible for keeping the mass moving in a circular path. In order to calculate the work done in 3/4th of rotation, we need to understand the relationship between work, force, and displacement.

Work Equation
The work done on an object is given by the equation:
Work = Force x Displacement x cos(θ)

Where:
- Work is the energy transferred to or from an object
- Force is the applied force on the object
- Displacement is the change in position of the object
- θ is the angle between the force vector and the displacement vector

Force in Circular Motion
In circular motion, the force acting on the mass is the centripetal force, given by:
Force = mass x acceleration

The centripetal acceleration is given by:
acceleration = (velocity^2) / radius

Where:
- mass is the mass of the object
- velocity is the speed of the object
- radius is the radius of the circular path

Displacement in Circular Motion
The displacement in circular motion is the distance traveled along the circumference of the circle. In 3/4th of a rotation, the displacement is equal to 3/4th of the circumference of the circle.

Calculating Work
To calculate the work done in 3/4th of rotation, we need to determine the force and displacement.

1. Calculate the centripetal force using the mass, velocity, and radius of the circular path.
2. Determine the displacement by multiplying 3/4th of the circumference of the circle by the radius.
3. Calculate the angle θ between the force and displacement vectors.
4. Substitute the values into the work equation: Work = Force x Displacement x cos(θ).
5. Calculate the work done in 3/4th of rotation.

Conclusion
In conclusion, the work done in 3/4th of rotation can be calculated by considering the centripetal force, displacement, and the angle between the force and displacement vectors. By applying the work equation, the value of work can be determined.

The work done on a body moving in a circular path is also zero. This is because, when a body moves in a circular path, then the centripetal force acts along the radius of the circle, and it is at right angles to the motion of the body.