Uniform Circular Motion

Circular MotionUniform circular motion occurs when an object travels in a circular path at a constant speed.

Uniform circular motion

Instantaneous velocity

acceleration

Q. Explain why a ball moving in a circle must be accelerating towards the centre.

A. - Magnitude of velocity is constant - Direction of velocity changes- Thus v is changing so it must be accelerating.

Centripetal force

Any acceleration must be caused by a force. In circular motion, centripetal acceleration is caused by the centripetal force (which acts towards the centre of the circle).

v

Centripetal force

Q. Explain what provides the centripetal force upon the following objects moving in circular motion:a. A planetb. An electronc. A cornering cyclistd. A banking aircrafte. ‘Wall of death’ motorcyclistf. The clothes in a spin drier

Circular Motion Calculations

Centripetal acceleration is calculated using the formula…

Thus, using F = ma

Note that using the speed formula we can say…where…

a = v2

r

v = tangential velocity at any instant (ms-1)r = radius of circle (m)a = centripetal acceleration (ms-2)

Centripetal force = mv2

r

v = 2πr T

T = 1 f

Q. What would be the effect of reducing the centripetal force for a car cornering at a fixed velocity?

E.g.1

A stone of mass 0.5kg on the end of a string 250cm long is swung in a horizontal plane at a constant speed of 10ms-1. What is the tension in the string?

A. F = mv2

r= 0.5 x 102

2.5= 20N

Vertical Circular Motion

When moving at a constant speed in a vertical circle, the centripetal acceleration and centripetal force must both be constant. A

D

C

B

mg

mg

mg

mg

T

TT

T

E.g. A bucket swinging vertically on a string:

At A:

The tension is smallest because part of the centripetal force is provided by the weight.

At C:

The tension is greatest because the tension must hold up the weight as well as supply the centripetal force.

At B and D:

The tension provides all of the centripetal force as the weight is perpendicular to the tension.

A

D

C

B

mg

mg

mg

mg

T

TT

T

At A:

mv2/r = mg + T

At C:

mv2/r = T – mg

At B and D:

mv2/r = T

Rollercoaster Physics

Q. Consider the forces acting on a rollercoaster at the top and bottom of its motion. Can you write equations describing the centripetal force similar to the last example?

B

A

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