Physics - Force, Work, Power and Energy

Moment of Force (Torque): The turning effect of a force about a fixed point or axis. It is calculated as the product of the force and the perpendicular distance from the axis of rotation: $\tau = F \times d$.

Principle of Moments: For a body in equilibrium, the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot: $\sum \text{Clockwise Moments} = \sum \text{Anticlockwise Moments}$.

Work: Work is said to be done only when a force applied on a body makes the body move. It is a scalar quantity defined as $W = Fs \cos \theta$, where $\theta$ is the angle between the force and displacement.

Power: The rate of doing work. It is the ratio of work done to the time taken: $P = \frac{W}{t}$. Its S.I. unit is the Watt ($1 \text{ W} = 1 \text{ J/s}$).

Energy: The capacity to do work. Mechanical energy exists in two forms: Potential Energy ($U$), due to position or configuration, and Kinetic Energy ($K$), due to motion.

Work-Energy Theorem: The work done by a force on a moving body is equal to the increase in its kinetic energy: $W = \Delta K = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$.

Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only be transformed from one form to another. In a conservative field (like gravity), the total mechanical energy ($K + U$) remains constant.

Units of Energy: Common units include the Joule ($J$), Calorie ($1 \text{ cal} = 4.18 \text{ J}$), Electron-volt ($1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$), and Kilowatt-hour ($1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$).