circular motion © david hoult 2009

Circular Motion

© David Hoult 2009

Acceleration of a Body Moving in a Circular Path at Constant Speed

The magnitude of the velocity of the body is constant but the direction is constantly changing, therefore, the body is

© David Hoult 2009


The magnitude of the velocity of the body is constant but the direction is constantly changing, therefore, the body is accelerating

At any instant, the direction of the velocity is a

© David Hoult 2009


The magnitude of the velocity of the body is constant but the direction is constantly changing, therefore, the body is accelerating

At any instant, the direction of the velocity is a tangent to the circular path

© David Hoult 2009

The magnitude of the acceleration depends on

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i) the speed of the body

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i) the speed of the body

ii) the radius of the circular path

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We might suggest that

a

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a v

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a v

and that

a

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a v

and that

a 1r

and therefore

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a v

and that

a 1r

Consideration of the units suggests that

and thereforea v

r

© David Hoult 2009


a v

and that

a 1r

Consideration of the units suggests that

and thereforea v

r

a v2

r© David Hoult 2009

It can be shown that the magnitude of the acceleration is given by

a = v2

r

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a = v2

r

or in terms of angular speed

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a = v2

r


a = r 2

or in terms time period

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a = v2

r


a = r 2

or in terms time period

a = 4 2 r

T2

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The direction of this acceleration is

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The direction of this acceleration is towards the centre of the circle

For this reason it is called a

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For this reason it is called a centripetal acceleration and is said to be caused by a centripetal force

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For this reason it is called a centripetal acceleration and is said to be caused by a centripetal force

Fc = m v2 r

Fc = mr2

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A centripetal force does not change the kinetic energy of the body on which it acts because it acts

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A centripetal force does not change the kinetic energy of the body on which it acts because it acts at 90° to the direction of the motion of the body

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Estimate the magnitude of the force needed to cause a car to move around a curve in a road at 50 km h-1.

What force causes the centripetal acceleration in this situation ?

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Friction

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Estimates needed:

Friction

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Estimates needed:

mass of car, m

Friction

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Estimates needed:

mass of car, m

radius of path, r

Friction

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Fc = m v2 r

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If the car turns to the left:

A small mass hangs on a string inside the car. It is observed by a passenger*.

* the mass is in front of the passenger.

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Find the angle during the time the car is moving round the curved path.

A small mass hangs on a string inside the car.


© David Hoult 2009

Te cos

mgTe sin

The vertical forces acting on the mass are in equilibrium, therefore

Te cos must have the same magnitude as mg

© David Hoult 2009

Te cos

mgTe sin

The mass is accelerating to the left, horizontally

The horizontal component of the tension provides the centripetal force needed for this acceleration.

© David Hoult 2009

circular motion © david hoult 2009

Documents

body david hoult

mrw2 david hoult

v david hoult

circular path david

centripetal force david

circular motion david

p2 rt2 david hoult

terms time period david