notes10 - Chapter 10 Rotational Kinematics Up to now we...

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Chapter 10. Rotational Kinematics Up to now, we have only considered point- particles, i.e. we have not considered their shape or size, only their mass Also, we have only considered the motion of point-particles – straight-line, free-fall, projectile motion. But real objects can also tumble, twirl, … This subject, rotation, is what we explore in this chapter and in Chapter 11. First, we begin by extending the concepts of circular motion
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Instead of a point-particle, consider a thin disk of radius r spinning on its axis x y z r θ This disk is a real object, it has structure We call these kinds of objects Rigid Bodies Rigid Bodies do not bend twist, or flex; for example, a billiard ball θ r r s s = arc length Axis of rotation r s = = radius length arc θ Units of radians (rad)
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θ r s = For one complete revolution rad 2 π θ = nce circumfere 2 = = r s π Conversion relation: 2 π rad = 360° Now consider the rotation of the disk from some initial angle θ i to a final angle θ f during some time period t i to t f z θ i θ f ccw x y Δ θ = θ f θ i θ f θ i t f t i = Δ θ Δ t = ω avg Angular displacement (units of rad, ccw is +) Average angular velocity (units of rad/s)
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Similar to instantaneous velocity, we can define the Instantaneous Angular Velocity A change in the Angular Velocity gives Analogous to Instantaneous Angular Velocity , the Instantaneous Angular Acceleration is ω = lim Δ t 0 Δ θ Δ t ω f ω i t f t i = Δ ω Δ t = α avg Average Angular Acceleration (rads/s 2 ) α = lim Δ t 0 Δ ω Δ t
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Actually, the Angular Velocities and Angular Acceleration are magnitudes of vector quantities What is their direction? They point along the axis of rotation with the sign determined by the right-hand rule Example A fan takes 2.00 s to reach its operating angular speed of 10.0 rev/s. What is the average angular acceleration (rad/s 2 )?
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