Physics Study Guide/Circular Motion

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[edit] Uniform Circular Motion

A two dimensional polar co-ordinate system

Uniform circular motion assumes that an object is moving (1) in circular motion, and (2) at constant speed v; then

where R is the radius of the circular path, and T is the time period for one revolution.

Any object travelling on a circle will return to its original starting point in the period of one revolution, T. At this point the object has travelled a distance 2πR. If T is the time that it takes to travel distance 2πR then the object's speed is

where

One point that has coordinate (x,y) is equivalent to a point (R,o) on the circle

R² = x² + y²

tanθ = y / x

y = R Sinθ

x = R Cosθ = R Sin (θ+90)

Therefore any periodic motion can be represented by a motion that has Amplitude varies with Time, Phase sinusoidally and can be expressed in mathematical function

F(t,R,θ) = R Sin (ωt + θ)

ω = 2πf

T = 1 / f

[edit] Rotational Kinematics

Rotational Kinematics concerns with the description of spinning bodies. The orientation of any object can be described by three angular quantities called the Euler angles.

A two dimensional polar co-ordinate system

A three dimentional spherical-polar co-ordinate system

Euler angles which uniquely describe the orientation of an object in space