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Physics - Circular Motion

declan barnes 10 years ago

Angles can take the form of Radians instead of Degrees
Radians are defined as the arc-length divided by the radius of the circle. This means that for a complete circle (360o) the arc-length is the circumference of the circle (2πr) divided by the radius (r), leaving a result of 2π. This means that 360o is equal to 2πc.

A common rule to convert degrees into radians is:
angle in radians = 2π/360 x angle in degrees

The Angular Speed is the angle an object rotates through per second
• Linear speed, v, is defined as distance/time, angular speed is defined similarly, with ω defined as angle/time. The unit of ω is rad s-1.
ω= θ/t
• The linear speed, v, and angular speed, ω, of a rotating object are linked with the equation:
v = ωr

Circular Motion has a Frequency and Period
• The frequency, f, is the number of complete revolutions per second (Hz)
• The period, T, is the time taken for a complete revolution (s)
• Frequency and period are linked by the equation:
f = 1/T
• For a complete circle, an object turns through 2πc in a time T, so frequency and period are related to ω by:
ω = 2πf and T = 2π/ω

Objects travelling in circles accelerate since their velocity is changing
• Even if the object is going at a constant speed, its velocity is changing since its direction is changing
• Since acceleration is defined as the rate of change of velocity, the car is accelerating even though it isn’t going any faster
• This acceleration is called centripetal acceleration and is always directed towards the centre of the circle.
• There are two formulas for centripetal acceleration:
a = v2/r and a = rω2

The Centripetal Acceleration is produced by a Centripetal Force
From Newton’s laws, if there’s a centripetal acceleration, there must be a centripetal force acting towards the centre of the circle.
Since F=ma, the centripetal force must be:
F = mv2/r and F = mω2r
The centripetal force is what keeps the object moving in a circle – remove it and the object would fly off at a tangent.