ERIC Circular Motion

RAW

Angular velocity

• The rate of change of the angle of an object moving in a circular path

• ω = θ/t = 2π/T = 2πf

Centripetal force

• A force keeping a body moving in uniform circular motion

• Always perpendicular to the velocity

• Examples: gravitational attraction, tension in a string, friction for a car in a bend

• F = mv²/r = mω²r

Linear velocity

• Velocity tangent to the circular path

• v = 2πr/T = rω

Centripetal acceleration

• Acceleration of any object travelling in uniform circular motion

• Always acts towards the centre of the circle

• a = v²/r = ω²r

Labelled diagram of the forces of a biker

• Weight component acting downwards

• Reactionary force N acting perpendicular the surface

• N_H is the horizontal component (mgcosθ)

Why do you feel more weightless on top of a Ferris wheel?

• At the top of the ride the normal contact force decreases

• Hence, the net force isn’t 0 and a shift in weight can be felt

Derive tanθ = v²/rg for a conic pendulum

• Tsinθ = mv²/r

• Tcosθ = mg

• tanθ = v²/rg