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# Circular Motion

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Explains circular motion and compared it to linear motion.
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• In the 5th slide
alpha = angular acceleration

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### Circular Motion

1. 1. Sautter 2015
2. 2. Circular Motion • Circular motion (rotation) can be measured using linear units or angular units. Angular units refer to revolutions, degrees or radians. • The properties of circular motion include displacement, velocity and acceleration. When applied to rotation the values become angular displacement, angular velocity or angular acceleration. Additionally, angular motion can be measured using frequencies and periods or rotation. • The Greek letters theta (), omega () and alpha () are used to represent angular displacement, angular velocity and angular acceleration. 2
3. 3.    3
4. 4. Circular Motion • The equations which describe angular motion are similar to those describing linear motion. Rotational equations can therefore be derived from linear equations by analogy (direct comparison). • Recall the following linear motion equations: • VAVERAGE = s/ t = (V2 + V1) / 2 • Si= V0 t + ½ at2 • Vi = VO + at • Si = ½ (Vi 2 – Vo 2) /a • Each of these can be converted to a rotational motion equation by substituting the rotational quantity in for the appropriate linear quantity. 4
5. 5. VAVERAGE = s/ t = (V2 + V1) / 2 AVERAGE =   /  t = (2 + 1) / 2 Si= V0 t + ½ at2  = o t + ½ t2 Vi = VO + at i = o + t Si = ½ (Vi 2 – Vo 2) /a I = ½ (i 2 - o 2) /  5
6. 6. The linear velocity of a body can be related to it angular velocity by the equation: V =  R Where V = linear velocity in m/s , ft/s, etc = angular velocity in radians/s R = the radius of the object in meters, feet, etc. The linear acceleration of a body can be related to it angular acceleration by the equation: a =  R Where a = linear acceleration in m/s2 , ft/s2, etc  = angular acceleration in radians/s2 R = the radius of the object in meters, feet, etc. 6
7. 7. Frequency & Period • Two other important quantities relating to circular motion are frequency and period. • Frequency refers to how often (frequently) an object rotates. If a body rotates 10 complete revolutions in 2 seconds the frequency of rotation is 10/2 or 5 revolutions per second. The unit “hertz” is use to represent cycles or rotations per second. Therefore, 5 revolutions per second is 5 hertz abbreviated as 5 Hz. • Period is the time for one complete cycle or revolution. If an object rotates at 5 revolutions per second (5 Hz) the each revolution takes 1/5 second or 0.20 seconds and the period then is 0.20 seconds. • The symbol for frequency is f. The symbol for period is T. Frequency and period are related to each other by the equation: f = 1/ T and T = 1 / f . 7