Torque, Kinetic Energy, Angular Momentum and Its Conservation

The change in the angle traced by the position vector of a particle about a fixed point when the particle moves along a curved path is called Angular Displacement. Its unit is radian (rad).

The angular displacement per unit time, i.e., \[\overline ω\] = Δθ/Δt, is called Angular Velocity. It is a vector quantity whose direction is normal to the rotational plane given by the right-hand screw rule.

The rate of change of angular velocity, i.e., α = dω/dt, is called Angular Acceleration. Average angular acceleration is \[\overline α\] = (ω₂ − ω₁)/(t₂ − t₁).

The turning effect of a force about an axis of rotation, given as the product of the magnitude of force and the perpendicular distance of the line of action of the force from the axis of rotation, is called Torque (or Moment of Force).

\[\vec{\tau}=\vec{r}\times\vec{F},\quad\tau=rF\sin\theta\]

The product of the linear momentum of a body and the perpendicular distance of the line of action of the linear momentum vector from the axis of rotation is called Angular Momentum.

L = Iω = mvr sin θ