Circular motion

What does motion in a circular path at a constant speed imply

There is acceleration and requires a centripetal force

Equation for magnitude of angular speed

w=v/r=2πf

Where does centripetal acceleration act

Always acts towards the center of the circle

What does angular displacement show

How far around the circumference an object will be after time, t, has passed

Angular displacement equation

θ=2πt/T=2πft

What does angular velocity tell us

How many radians an object is passing through each second

Angular displacement per second

Angular velocity equation

w=2π/T=2πf

What is 1 radian

The angle that is formed when the length of the arc is equal to the length of the radius

What is circumference equal to

2πr

What is T

Time for one full rotation T=1/f

Speed equation

V=2πr/T=2πrf

Acceleration equation

a=v²/r

Gravitational force F equations

Gm1m2/r² = mv²/r

Equation derivatives

What happens to charged particles in a magnetic field

A charged particle moving in a uniform magnetic field will experience a force at right angles to it's motion (Flemming's LHR). This causes particle to exhibit circular motion

Equation for particle in a magnetic field

F=BeV

For motion of a car over hill above certain v what happens to s

S tends to zero and veichle loses contact with the road

What happens to motion of a car over a hill

• Weight keeping car moving in a circular motion

• Support force in opposite direction

• Resultant force between mg + s provides resultant centripetal force

Equations for motion of a car over a hill

Mg - s = mv²/t

S = mg - mv²/r

What happens on a banked track

• Without banking centripetal force is only provided by friction

• By banking it makes the horizontal component of support force acts as the centripetal force

Equation for banked track

V² = grtanθ

What happens on roundabouts (force of friction)

• Force of friction keeps car moving in circular motion

• If not high enough veichle moves in a straight line

Equation for force of friction

V0=(µgr)^1/2

What happens with the motion of rollercoaster

• Support force S is keeping the car moving in circular motion

• Weight is in the opposite direction

• Resultant force between S and mg provides a resultant centripetal force

• At bottom feel heavier as support force must increase to keep moving in circular motion

Equation for motion of a rollercoaster

S - mg = mv²/r

S = mg + mv²/r