Uniform circular motion Uniform circular motion is motion along a circular path in which there is no change in speed, only a change in direction. v FcFc

 Objects moving in uniform circular motion will have a constant speed. But does this mean that they will have a constant velocity?  Recall that speed and velocity refer to two distinctly different quantities. Speed is a scalar quantity and velocity is a vector quantity.scalar quantityvector quantity  Velocity, being a vector, has both a magnitude and a direction. The magnitude of the velocity vector is the speed of the object. The direction of the velocity vector is directed in the same direction that the object moves.  Since an object is moving in a circle, its direction is continuously changing. The best word that can be used to describe the direction of the velocity vector is the word tangential.

A tangent line is a line that touches a circle at one point but does not intersect it. Click below! Cool demo of tangential velocity vectors in circular motion! Cool demo of tangential velocity vectors in circular motion! Cool demo of tangential velocity in circular motion Cool demo of tangential velocity in circular motion

 We usually think of acceleration as a change in speed.  Because velocity includes both speed and direction, acceleration can also be a change in the direction of motion.

 An object moving in a circle at constant speed is accelerating. It is accelerating because the direction of the velocity vector is changing.

 What direction would the force have to be in to make the object change from one of these vectors to the next one?

 Any force that causes an object to move in a circle is called a centripetal force.  A centripetal force is always perpendicular to an object’s motion, toward the center of the circle.

 Can you see that the force that makes an object continuously change its direction by going in a circle must be towards the center of the circle?

When you swing a ball around on a rope, you must hold onto the rope and pull on it with a force. Otherwise the ball and rope will fly off according the Law of Inertia, which wants to have an object move in a straight line. The force you are pulling on the rope is the centripetal force. If you’re solving a problem and you’re asked to find the tension in the rope, you find the centripetal force.

 For a car going around a curve, the centripetal force has to be supplied by the friction between the tires and the road.  A prior concept, coefficient of friction, is going to reappear in these problems!

 The Moon is kept in orbit around the Earth through centripetal force caused by the constant gravitational force between the Moon and the Earth.  If the gravitational force would suddenly vanish, the Moon would shoot off in a straight line, tangent to its previous orbit around the Earth.

Check Your Understanding An object is moving in a clockwise direction around a circle at constant speed Which vector below represents the direction of the force vector when the object is located at point A? 2. Which vector below represents the direction of the force vector when the object is located at point C? 3. Which vector below represents the direction of the velocity vector when the object is located at point B? 4. Which vector below represents the direction of the velocity vector when the object is located at point C? 5. Which vector below represents the direction of the acceleration vector when the object is located at point B?

 If the force is towards the center, the acceleration must also be towards the center.

 Acceleration is the rate at which an object’s velocity changes as the result of a force.  Centripetal acceleration is the acceleration of an object moving in a circle due to the centripetal force.

Consider ball moving at constant speed v in a horizontal circle of radius R at end of string tied to peg on center of table. (Assume zero friction.) R v

R v Two Equations for this unit:

R v m R = 5 m; v = 8 m/s m = 3 kg F = (3 kg)(12.8 m/s 2 ) F c = 38.4 N

m = 60.0 kg 450 N 30 m v = 15 m/s R FcFc m=? Speed skater Draw and label sketch

Newton’s 2nd law for circular motion: r = 2.13 m Draw and label sketch r = ? m = 80 kg; v = 4 m/s 2 F c = 600 N

Centripetal acceleration: