Aim: How can we describe circular motion? Circular Motion

How can we describe circular speed? If this is true, why does ANYTHING move in a circle? Objects traveling in circular motion have SPEEDHow do we define SPEED? What ‘d’ are we talking about? CIRCUMFERENCE C = 2πr = πd What ‘t’ are we talking about? PERIOD (T) Time for one revolution Velocity is TANGENT to the circle at ALL POINTS

How can we define centripetal force? Inertia causes objects to travel STRAIGHT Paths can be BENT by FORCES CENTRIPETAL FORCE bends an object’s path into a CIRCLE -- pulling toward the CENTER

Misconception The doors to the “Gravitron” close and it starts to spin. You are pushed against the outside edge of the ride and pinned there, You must be experiencing “centrifugal force” throwing you outward from the ride! Right?

Can you explain what is really happening? As the Gravitron starts to spin, friction between your body and the ride start you moving Once you are moving, your body wants to go STRAIGHT … but you can’t… The WALLS push you back in toward the center of the ride! vcvc FcFc

What is it you feel? centrifugal (center fleeing) force –A ‘fictitious’ or ‘inertial’ force that is experienced from INSIDE a circular motion system centripetal (center seeking) force –A true force that pushes or pulls an object toward the center of a circular path

How can we calculate Centripetal Acceleration? Unbalanced forces cause ACCELERATION v, F c, and a c constantly CHANGE DIRECTION, but not MAGNITUDE Centripetal force provides an unbalanced, net force toward the center of a circular path

Example #1 Determine the centripetal acceleration of a toy ball swinging with a speed of 12 meters per second on the end of a 1.44 meter long string. a c = v 2 / r a c = (12 m) 2 / (1.44 m) a c = 100 m/s 2

Example #2 Determine the velocity of a car that experiences a centripetal acceleration of 6 meters per second 2 as it moves through a turn with a radius of 5 meters. a c = v 2 / r 6 m/s 2 = v 2 / (5 m) v = 5.48 m/s

Calculating F c Newton’s 2 nd Law? F = ma

Example #3 What is the centripetal force on a 2000 kilogram airplane making a turn with a radius of 1000 meters if it is moving at 300 meters per second? F c = mv 2 / r F c = (2000 kg) (300 m/s) 2 / (1000 m) F c = 180,000 N

Example #4 How far from the center of a merry-go-round is a 500 kilogram horse that is traveling at 3 meters per second if it experiences a force of 3000 newtons? F c = mv 2 / r 3000 N = (500 kg) (3 m/s) 2 / r r = 1.5 m