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Further mechanics extends the principles of Year 1 to cover circular motion and oscillatory systems. These concepts are essential for understanding everything from satellite orbits to musical instruments, and from suspension bridges to radio tuning circuits.
When an object moves in a circle at constant speed, its velocity is constantly changing direction. This means the object is accelerating, even though its speed is constant. The acceleration is always directed towards the centre of the circle.
Key Definition: Angular velocity (ω) is the rate of change of angular displacement, measured in rad s⁻¹.
ω = 2π/T = 2πf = Δθ/Δt
where T is the period and f is the frequency.
The linear speed of an object moving in a circle of radius r is:
v = ωr
The acceleration is always directed towards the centre of the circle:
a = v²/r = ω²r
By Newton's second law, a resultant force must act towards the centre to maintain circular motion:
F = mv²/r = mω²r
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