Centripetal Force Acceleration in a Circle dq Acceleration

Acceleration in a Circle dq ] Acceleration is a vector change in velocity compared

Centripetal Acceleration ] Uniform circular motion takes place with a constant speed but changing

Buzz Saw ] A circular saw is designed with teeth that will move at

Law of Acceleration in Circles ] ] Motion in a circle has a centripetal

Conical Pendulum ] A 200. g mass hung is from a 50. cm string

Radial Net Force ] ] The mass has a downward gravitational force, -mg. There

Acceleration to Velocity ] The acceleration and velocity on a circular path are related.

Period of Revolution ] The pendulum period is related to the speed and radius.

Radial Tension ] The tension on the string can be found using the angle

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Centripetal Force

Acceleration in a Circle dq ] 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.

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. ] • r = v 2/a. ] ] The bonds that hold the cutting tips can withstand a maximum acceleration of 2. 0 x 104 m/s 2. Start with a = v 2/r. Substitute values: • r = (40. m/s)2/(2. 0 x 104 m/s 2) • r = 0. 080 m. ] Find the diameter: • d = 0. 16 m = 16 cm. ] Find the maximum diameter of the blade.

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 FT cos q 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!