Uniform CM

Overview

A particle is in uniform circular motion if it travels around a circle or a circular arc at constant, or uniform, speed. Even though the speed does not vary within the particle, the particle is still accelerating. We think of acceleration, or change in velocity, as an increase or decrease in speed. However, velocity is a vector. So even if velocity changes only in direction, an acceleration remains, and that is the basic concept of Uniform Circular Motion. If the acceleration of the particles is directed inward, we call it centripetal acceleration meaning center seeking acceleration. Centripetal acceleration can only exist for objects moving along a circular orbit. In addition, at any point during the objects acceleration at constant speed, the particle can travel the circumference of the circle in time T. This time T is called the period of revolution, or period. Period is the time for a particle to go around a closed path exactly once.

Equations

Equation One

a=v^2/ r (centripetal acceleration)
r= radius of the circle, v=speed of the particle

Equation Two

T= 2(pi)r/v
2(pi)(r)=circumference of the circle, v= speed of the particle

++Equation Three
F=mv^2/ R
m=massof object, v=speed of the object, R=radius. The vector quantities a and F are directed toward the center of curvature of the particles path.

What is the centripetal acceleration, in g units, of a pilot flying a plane at speed v= 2500 km/h or (694 m/s) through a circular arc with radius of curvature r=5.80km?


a= v^2/ r
a= (694 m/s)^2/ 5800m
a=83.0m/s/s=8.5g

Evaluate the period for a car moving around a track of diameter 6 m at speed v= 10m/s.


T= 2(pi)r/v
T=2(pi)(3m)/ 10m/s
T=1.885s

Special Cases

If a particle moves in a circle or a circular arc with radius R at constant speed v, it is said to be in uniform circular motion. It then has a centripetal acceleration a with magnitude given by a= v^2/ R. This acceleration is due to a net centripetal force on the particle, with magnitude given by F=mv^2/ R.

Joke

What did the plug say to the socket?

Socket to me baby!!!

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