Circular Motion and Gravity Circular Motion n n

Circular Motion and Gravity

Circular Motion n n Motion at constant speed around uniform circle n Car going around curve n Satellite in orbit n Spinning fan blade Linear units m/s & m/s 2 not rpm & rad/s

Circular or Curved Motion n n Any motion other than in a straight line May be at constant speed

What is the path of a moving object if net force is zero? A. B. C. A circle An ellipse A straight line 0% 0% 0% A circle An ellipse A straight line

Which law of Newton describes this? A. B. C. Newton’s First Law Newton’s Second Law Newton’s Third Law 0% 0% 0% Newton’s First Newton’s Third Law Second Law

If a body travels in a curve its motion must be 0% Ac c el er at ed ro st a 0% Ze 0% nt 0% Co n D. cle C. cir B. A circle Constant Zero Accelerated A A.

Body moving in a circle

Body moving in a circle n n Velocity changes direction What direction is the change?

Circular motion

Body moving in a circle

Body moving in a circle n Velocity changes toward the center of the circle (curve) n n n Centripetal acceleration Velocity is always changing for circular motion There is always an acceleration

Newton’s First Law n No net force: moving body moves With constant speed n In straight line n

An object is whirled on a string. If the string breaks what direction does the object go? A. B. C. D. 1 2 3 4 0% 0% 1 2 3 4

Centripetal Acceleration n Center-directed

Centripetal Acceleration n An object travels in a circle at a constant speed…

For constant speed does the magnitude of the acceleration change? A. B. Yes No 0% 0% Yes No

For constant speed does the direction of the acceleration change? A. B. Yes No 0% 0% Yes No

Centripetal Acceleration n Acceleration = Dv/Dt = (vf – vi)/(tf - ti) No change in |v| n Change in direction n Velocity tangent to circle Acceleration toward center of circle n a is constantly changing

Centripetal Acceleration n a = v 2/r Newton’s Second Law n F = ma Centripetal force n F = mv 2/r

Centripetal Force n n Equations tell the size of the acceleration or the force What produces the force?

Centripetal Force n The Force is what gives a Jedi his power. Its an energy field created by all living things. It surrounds us and penetrates us. It binds the galaxy together.

Centripetal Force mv 2/r = gravity n mv 2/r = tension n mv 2/r = friction The force can come from n n Friction n Rope n gravity n

Centripetal Acceleration n n A car drives around a 20 m radius circle at a speed 10 m/s. What is the acceleration of the car?

What is the acceleration of the car? A. B. C. D. 0. 5 m/s 2 10 m/s 2 20 m/s 2 0% 0% 0. 5 m/s 2 10 m/s 2 20 m/s 2

Centripetal Acceleration n A car drives around a 20 m radius circle at a speed 10 m/s. n What is the acceleration of the car? n v 2/r = (10 m/s)2/20 m = 5 m/s 2

Centripetal Force n n n Two identical cars drive around a circle. Car A drives twice as fast as car B What is the ratio of the forces (FA/FB) needed to keep the cars going in circles Which force is bigger? How much bigger?

Force. A/Force. B A. B. C. D. E. FA = F B FA = 2 FB 2 FA = FB FA = 4 FB 4 FA = FB 0% 0% 0% FA = FB FA = 2 FB 2 FA = FB FA = 4 FB 4 FA = FB

Centripetal Force n n n Two cars drive at identical speeds around a circle. Car A has twice the mass of car B What is the ratio of the forces (FA/FB) needed to keep the cars going in circles Which force is bigger? How much bigger?

Force. A/Force. B A. B. C. D. E. FA = F B FA = 2 FB 2 FA = FB FA = 4 FB 4 FA = FB 0% 0% 0% FA = FB FA = 2 FB 2 FA = FB FA = 4 FB 4 FA = FB