A body free to rotate about an axis can make angular oscillations. For example, a photo frame or a calendar suspended from a nail on the wall. If it is slightly pushed from its mean position and released, it makes angular oscillations.
Conditions for an Angular Oscillation to be Angular SHM
The body must experience a net Torque that is restoring in nature. If the angle of oscillation is small, this restoring torque will be directly proportional to the angular displacement.
Τ ∝ – θ
Τ = – kθ
Τ = Iα
α = – kθ
This is the differential equation of an angular Simple Harmonic Motion. Solution of this equation is angular position of the particle with respect to time.
θ=θ0sin(ω0t+ϕ)
Then angular velocity,
ω=θ0.ω0cos(ω0t+ϕ)
θ0 – amplitude of the angular SHM
Example:
- Simple pendulum
- Seconds pendulum
- The physical pendulum
- Torsional pendulum