Circular Motion: Flashcards
Define uniform circular motion:
An object rotating at a steady rate.
Equation for circumference of a circle?
2pi * r
Prove that speed in circular motion = 2pi *r/T
circumference over time = speed = 2pi*r/T
Define angular displacement:
The angle the object has moved to.
Define angular speed:
The angular displacement per second.
Prove that distance = angle*radius
s = vt = 2pirt/T. since 2pit/T is = angle
then s= angleradius.
Give the equation for angular displacement.
Angle = 2pit/T = 2pif*t
Prove that angular speed = 2pi*f
angular speed = angle/time = (2pit/T)/t = 2pi/T =2pif
What is the unit of circular motion?
rad s^-1
Why is an object moving in circular motion accelerating?
Despite the magnitude of velocity remaining constant, the direction of velocity is changing so it is accelerating.
What is the equation for centripetal acceleration?
a=v^2/r
Define centripetal force:
The resultant force of an object moving around a circle at constant speed.
Prove centripetal force = mv^2/r
a= v^2/r so F=ma can be rewritten as mv^2/r or m *centripetal speed^2 *r
Why does a car lose contact with the surface of a bridge at the top if it goes too fast?
The resultant of the weight and the reaction force should be equal to the centripetal force i.e. mg - R = mv^2/r at the top of the hill as all of the weight is acting towards the centre of the curvature of the bridge. When it loses contact, R = 0 so mg = mv^2/r so sqrrt(gr) = v which is the speed it loses contact at. (???) It loses contact because at the top of the bridge the reaction force is equal to the centripetal force (mg) so it stops moving with circular motion momentarily and can lose contact with the road (???)
Why does a car skid if it turns a corner too fast?
Friction is the centripetal force. If v is too high, the centripetal force exceeds a certain value which means it skids as friction is too high.
