Centripetal Force

Acceleration in a Circle Acceleration is a vector change in velocity compared to time. For small angle changes the acceleration vector points directly inward. This is called centripetal acceleration. dq

Centripetal Acceleration Uniform circular motion takes place with a constant speed but changing velocity direction. The acceleration always is directed toward the center of the circle and has a constant magnitude.

Buzz Saw A circular saw is designed with teeth that will move at 40. m/s. The bonds that hold the cutting tips can withstand a maximum acceleration of 2.0 x 104 m/s2. Find the maximum diameter of the blade. Start with a = v2/r. r = v2/a. Substitute values: r = (40. m/s)2/(2.0 x 104 m/s2) r = 0.080 m. Find the diameter: d = 0.16 m = 16 cm.

Law of Acceleration in Circles Motion in a circle has a centripetal acceleration. There must be a centripetal force. Vector points to the center The centrifugal force that we describe is just inertia. It points in the opposite direction – to the outside It isn’t a real force

Conical Pendulum A 200. g mass hung is from a 50. cm string as a conical pendulum. The period of the pendulum in a perfect circle is 1.4 s. What is the angle of the pendulum? What is the tension on the string? q FT

Radial Net Force The mass has a downward gravitational force, -mg. There is tension in the string. The vertical component must cancel gravity FTy = mg FT = mg / cos q FTr = mg sin q / cos q = mg tan q This is the net radial force – the centripetal force. q FT cos q FT FT sin q mg

Acceleration to Velocity The acceleration and velocity on a circular path are related. q FT r mg tan q mg

Period of Revolution The pendulum period is related to the speed and radius. q L FT r mg tan q cos q = 0.973 q = 13°

Radial Tension The tension on the string can be found using the angle and mass. FT = mg / cos q = 2.0 N If the tension is too high the string will break!