Lecture 19 - University of Oklahoma

[Pages:14]Physics 2514

Lecture 19

P. Gutierrez

Department of Physics & Astronomy University of Oklahoma

Physics 2514 ? p. 1/14

Goals

Start the discussion of circular motion. We will define the kinematic variables needed to describe circular motion.

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Circular Motion

We will start with the case of uniform circular motion. (This refers to circular motion with a constant speed.)

Some definitions Period (T ) time interval to complete one orbit, therefore speed is given by

v

=

circumference period

=

2r T

r is the radius of the circle.

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Circular Motion

Some definitions--Use angular variables to measure position

s (radians) = r

full circle = 2

increases in counter-clockwise direction decreases in clockwise direction. measured from x axis

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Circular Motion

Some definitions--Use angular variables to measure speed

Angular Velocity

average

=

t

=

lim

t0

t

=

d dt

> 0 motion counter-clockwise < 0 motion clockwise

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Angular Position vs. Time

Slope of angular position vs. time plot gives angular velocity vs. time plot.

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Clicker

A particle moves clockwise around a circle at constant speed for 2.0 s. It reverses direction and moves counter clockwise at half the original speed until it has traveled through the same angle. Which is the particles angle-versus-time graph?

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Kinematic Equations

For uniform circular motion is constant. From definition of angular velocity

d

=

dt

f

tf

d = dt = f = 0 + (tf - t0)

0

t0

Take t0 = 0, tf = t, then

(t) = t + 0

Tangential acceleration is zero (acceleration in direction objects moves).

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