Circular motion

Define the radian

Angle subtended at the center of a circle by an arc of length equal to the radius of the circle

Equation for linear speed (in terms of angular speed and radius)

v = wr

Link between angle, radius and arc length

l = r x angle)

Angular displacement

Angle of an arc through which the object has moved from its starting position

Angular speed

the angle an object moves through per unit time (rate of change of angle)

• angular displacement per unit time

Angular acceleration

Force required for angular displacement

Equation for angular speed (angle and time)

w = change in angle/time

Equation for angular speed (Period)

w = 2(pi)/T (period)

OR

w = 2(pi)n/total time

Centripetal acceleration facts

• Object in circular path has constant changing velocity and is therefore accelerating

1st law = acceleration must have a resultant force, so centripetal force is the force experience during centripetal acceleration

• Centripetal force is perpendicular to motion of object, always acting inwards to center of the circle

Centripetal acceleration

Acceleration of an object towards the center of the circle when the object is rotating at constant speed round that circle

Reason for centripetal force

Velocity is a vector and is constantly changing

Newton’s first law motion = at rest/uniform velocity unless acted on by resultant force

resultant force is centripetal force (towards center of circle)

Centripetal force

Resultant force on an object towards the center of the circle when the object is rotating round that circle at constant speed

Velocity and acceleration - uniform circular motion

Constant magnitude of velocity, acceleration perpendicular to velocity (inwards)

• Acceleration in same direction as change in velocity, acceleration same direction as centripetal force F = ma

Centripetal acceleration equations

a = v²/r

OR

a = w²r

Centripetal force equation

F = (mv²)/r

OR

F = mw²r

(As F = ma)

Conversion from radians to degrees

x 180/(pi)

Centripetal force facts

• Is resultant force inwards

• If at constant speed, resultant force for vertical circle is constant —> Tension changes (least at top)

Conical centripetal motion

Horizontal component of tension is centripetal force

• If tension at top is 0, weight = centripetal force, centripetal acceleration = g