Further Mechanics Flashcards
Uniform circular motion
An object rotating at a steady rate.
Velocity of a point on the perimeter of a wheel undergoing uniform circular motion
v = 2πr / T = 2πrf
Angular displacement, θ (rad) in time t
θ = 2πt / T
Angular speed definition
The angular displacement per second.
Angular speed, 𝜔
𝜔 = 2π / T = 2πf
Centripetal acceleration
a = v^2 / r
Centripetal force
F = mv^2 / r
Simple harmonic motion definition
Oscillating motion in which the acceleration is proportional to and always in the opposite direction to the displacement.
Light damping
Occurs when the time period is independent of the amplitude so each cycle takes the same length of time as the oscillations die away.
Critical damping
Just enough to stop the system oscillating after it has been displaced from equilibrium and released. The oscillating system returns to equilibrium in the shortest possible time without overshooting.
Heavy damping
Occurs when the damping is so strong that the displaced object returns to equilibrium much more slowly than if the system is critically damped, no oscillating motion occurs.
Periodic force
Force applied at regular intervals.
Natural frequency
A system’s frequency when it oscillates without a periodic force being applied.
Forced vibrations
When an oscillating system experiences a periodic force.
Resonance
Occurs when the periodic force is exactly in phase with the velocity of the oscillating system.
