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MODULE 5

ADVANCED MECHANICS

SUMMARY: MOTION IN A CIRCLE

Syllabus Equations

Motion in a circle: centripetal acceleration / centripetal force

Tangential velocity (speed)

Angular speed (frequency)

Note: The equation should have been expressed as

Torque

Note: is better

Cross product

The vector product or cross product of two vectors and

Magnitude of the vector .

is a unit vector perpendicular to both the vectors and .

Right-hand screw rule

Torque (tau) S.I. unit N.m

Forces tend to change the motion of things

Torques rotational counterpart of forces

tend to twist or change the state of rotation of things

Applied torque

Applied force

Lever arm vector displacement from pivot to point of application of the force

Angle between the vectors and

Magnitude

component of applied force at right angles to the radius vector

Direction of the torque given by right-hand screw rule

Torque is perpendicular to both the radius vector and the force

Motion in a circle

Equation of a circle

Angular displacement [rad]

Angular speed [rad.s^-1]

Tangential velocity [m.s^-1]

(direction: tangent to circle)

Centripetal acceleration [m.s^-2]

(direction: towards centre of circle / perpendicular to circle)

A force must be applied to an object to give it circular motion. This net force is called the centripetal force.

(direction: towards centre of circle / perpendicular to circle)

Period T [s] time for 1 revolution

Frequency f [Hz] revolutions per seconds

Angular frequency (speed) [rad.s^-1]

Work W = 0

Banked curves

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Ian Cooper School of Physics University of Sydney

If you have any feedback, comments, suggestions or corrections please email Ian Cooper

ian.cooper@sydney.edu.au