Circular Motion Constant speed but accelerating Velocity is

Circular Motion

Constant speed but accelerating? ? Ø Velocity is a vector. The speed (magnitude) may remain the same but the direction can change. Ø Any change in velocity is caused by an acceleration. Ø Circular path changes direction of velocity. Ø Moving at a constant speed in a circle is called uniform circular motion (UCM).

v 1 position vector r 1 v 2 r 2

Centripetal Acceleration Ø Centripetal acceleration is the acceleration of an object in UCM. Ø This acceleration always points to the middle of the circle. Ø ac = v 2 r Ø Units are still m/s 2

Finding v Ø v = d/t Ø t is equal to the period (T): time for one full revolution. Ø d is the distance around the circle Ø Circumference equals 2πr Ø So v = 2πr T

Centripetal Force If an object is accelerating, there must be a net force in the direction of the acceleration, toward the center of the circle. Ø Newton’s 2 nd Law says F=ma Ø Fc = mac or Ø Fc = mv 2 r Ø Animation Ø

Putting centripetal force to work. Ø When a car travels around a corner the net force is the friction between the car and tires. This changes the direction of the cars velocity. Ø If the road is icy the centripetal force decreases and the velocity will not change direction. The car will move straight off the road. Ø Animation

Where Else Do We See This? Ø Discus Ø Hammer Throw Ø http: //www. youtube. com/watch? v=2 y- q 8 i. EIp. D 4 Ø Ride

The Fake Force Ø When a person driving slams on the brakes you move forward, the force and acceleration act in the opposite direction you move. Inertia makes you move forward. Ø Centrifugal force which makes you feel like you are being pushed against the outside of a circular moving object is just inertia. It is a nonexistent force.

Practice Ø A. 3 kg ball on a 1. 2 m string is traveling in a horizontal plane at 6. 1 m/s. l l Find the centripetal acceleration. Find the centripetal force.

One More Ø A car with a mass of 1500 kg travels around a curve with a radius of 45 m. The car is traveling at a speed of 20 m/s. l l l Find the centripetal acceleration of the car Find the centripetal force acting on the car Find the force of friction acting on the car.