Angular Motion

The unit for angular velocity is radian per second

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Unformatted text preview: ecause the particles are all locked together. The unit for angular velocity is radian per second (rad/s). If a particle moves in translation along the x axis, its linear velocity v is either positive or negative, depending on whether the particle is moving in the positive or negative direction of the axis. 3 Similarly, the angular velocity ω of a rotating rigid body is either positive or negative, depending on whether the body is rotating counterclockwise (positive) or clockwise (negative). The magnitude of the angular velocity is called the angular speed, which is also represented with ω. 2.5 Angular Acceleration If the angular velocity of a rotating body is not constant, then the body has an angular acceleration. Let ω1 and ω2 be its angular velocities at times t1 and t2, respectively. The average angular acceleration of the rotating body in the interval from t1 to t2 is defined as ∆ ∆ (9) where Δω is the change in angular velocity that occurs during the time interval Δt. The (instantaneous) angular acceleration α is lim ∆ ∆ ∆ (10) or for those who have had calculus (11) Just as for the angular velocity, equations (9)-(11) hold for every particle of that body. The unit of angular acceleration is radian per second-squared (rad/s2). 2.6 Angular Velocity as a Vector The magnitude of ω of the angle gives the change in the angular displacement per unit time; the sign gives us the sense of rotation. Because there is an axis associated with every rotation and there are two directions associated with every axis, we can associate the two possible senses of rotation unambiguously. All we need is a convention known as the right hand rule (See Figure 3): 1. Curl your right hand so that your hand curls in the same way as the rotation. 2. Stick out your thumb. 3. The direction of the thumb corresponds to the direction of the angular velocity vector. Thus by using this rule counterclockwise rotation in the plane of this paper will have a ω that is out of this paper. Likewise, clockwise rotation in the plane of this paper will have a ω into this paper. 4 Figure 3 Demonstration of the right hand rule 2.7 Relations between Angular and Linear Variables Consider the case of uniform circular motion, in which a particle travels. When a rigid body rotates around an axis, each particle in the body moves in its own circle around that axis. Since the body is rigid, all the particles make one revolution in the...
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This document was uploaded on 03/20/2014 for the course PHYS 215 at Lafayette.

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