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chapter07

# chapter07 - Chapter 7 Rotational Motion and The Law of...

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Chapter 7 Rotational Motion and The Law of Gravity

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The Radian The radian is a unit of angular measure The radian can be defined as the arc length s along a circle divided by the radius r s r

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Angular Displacement Axis of rotation is the center of the disk Need a fixed reference line During time t, the reference line moves through angle θ
Rigid Body Every point on the object undergoes circular motion about the point O All parts of the object of the body rotate through the same angle during the same time The object is considered to be a rigid body This means that each part of the body is fixed in position relative to all other parts of the body

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Angular Displacement, cont. The angular displacement is defined as the angle the object rotates through during some time interval The unit of angular displacement is the radian Each point on the object undergoes the same angular displacement f i
Average Angular Speed The average angular speed, ω, of a rotating rigid object is the ratio of the angular displacement to the time interval f i av f i t t t

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Angular Speed, cont. The instantaneous angular speed is defined as the limit of the average speed as the time interval approaches zero Units of angular speed are radians/sec rad/s Speed will be positive if θ is increasing (counterclockwise) Speed will be negative if θ is decreasing (clockwise)
Average Angular Acceleration The average angular acceleration of an object is defined as the ratio of the change in the angular speed to the time it takes for the object to undergo the change: f i av f i t t t

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Angular Acceleration, cont Units of angular acceleration are rad/s² Positive angular accelerations are in the counterclockwise direction and negative accelerations are in the clockwise direction When a rigid object rotates about a fixed axis, every portion of the object has the same angular speed and the same angular acceleration
Angular Acceleration, final The sign of the acceleration does not have to be the same as the sign of the angular speed The instantaneous angular acceleration is defined as the limit of the average acceleration as the time interval approaches zero

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Analogies Between Linear
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chapter07 - Chapter 7 Rotational Motion and The Law of...

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