For an object travelling in circular motion, the angular displacement is the angle covered by the body in radians and it is calculated using the formula θ = arc/radius. The angular displacement can then be used to find the angular speed of an object using the formula ω = θ/t. Angular speed is given in rad/s.

An object moving in circular motion is accelerating since it has a changing velocity. This is because of the fact that the direction of the object is changing since it is moving in a circle. Centripetal acceleration can be caluclated using the following formula: a = v²/r = ω²r.

Simple harmonic motion is a type of oscillation that only occurs when the following two conditions are met:
1. The acceleration of the object must be directly proportional to its displacement from its equilibrium position,
2. The acceleration must always be directed towards the equilibrium position.

The magnitude of simple harmonic acceleration can be calculated using the following formula: acceleration = (2π × frequency)² × displacement.

An object oscillating in simple harmonic motion reaches maximum speed at the equilbrium position. In this position, the acceleration of the objetct is 0. At maximum amplitude, the object has a velocity of 0, however has a maximum acceleration. The maximum speed reached by the object can be calculated using the following formula: maximum velocity = A × 2πf, where A = amplitude.

Maximum acceleration occurs at maximum amplitude.
a = (2πf)² × x
maximum acceleration = (2π × 5 Hz)² × 0.07 m = 69.1 m/s²

69.1 m/s²

v = A × 2πf
v = 0.03 m × 2π × 2 Hz
v = 0.377 m/s (to 3 significant figures)

0.377 m/s

θ = arc ÷ radius
angular displacement = 0.8 m ÷ 1.2 m = 0.667 rad (to 3 significant figures)

0.667 rad

a = (2πf)² × x
6 m/s² = (2π × f)² × 0.09 m
f = 1.30 Hz (to 3 significant figures)

1.30 Hz

v = rω
5 m/s = 22 m × ω
angular speed = 0.227 rad/s (to 3 significant figures)
ω = θ/t
0.227 rad/s = θ/38 s
angular displacement = 8.64 rad (to 3 significant figures)

8.64 rad