Circular Motion

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Circular Motion

Centripetal Acceleration

A stone is whirled round on the end of a 1.5 m long piece of string. If the acceleration of the stone is 3g (30 m/s2) calculate the speed at which the stone is moving. Use: a = v2/r so v2 = ar = 30x1.5 = 45 and so v = [45]1/2 = 6.7 m/s

We call the acceleration of an object moving in uniform circular motion—resulting from a net external force—the centripetal acceleration.

CENTRIPETAL ACCELERATION = v2/r

1. Size is constant 2. Direction is towards the centre of the circular path

Vertical Circular Motion

Examples

A body revolves in a vertical circle such that its motion at different points is different then the motion of the body is said to be vertical circular motion.

Acceleration

Speed

Net Force

Centripetal Force

A motorbike and rider of total mass 100 kg travel round a roundabout of radius 8 m at a speed of 4 m/s. . What is the centripetal force needed to do this? F = mv2/r = [100 x 42]/8 = 200 N.

Features

2. Direction is towards the centre of the circular path

1. Size is constant

Formula

Is a force pushing or pulling the object towards the center of the circle.

The unbalanced force acing on an object in uniform circular motion is called Centripetal force, Fcent

Banked Curves

Example

A banked surface is one that slopes upward towards the outer edge of a curve. Banked surfaces exist at on-ramps to highways because cars have to start traveling faster to enter the highway.

A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn.

Angular Velocity

Meaning

"Angular velocity" is a measure of turning per time unit. It tells you the size of the angle through which something revolves in a given timespan

Formulas