Chapters 9 & 10

Chapters 9 & 10 - Rotation and angles Chapters 9 and...

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1 Chapters 9 and 10: Rotational Motion We’ve considered the physics of the motion of particles , and the motion of the center of mass of extended objects. But extended objects can also rotate about an axis. Rotation and angles Think about a rigid body that rotates about a fixed axis . First, we need to sort out a better ‘unit’ for angles We’ve been using degrees [0:360], but there is a better ‘unit’ we can use called radians 1 radian is defined as the angle subtended at the center of a circle by an arc with length equal to the radius of the circle all round the circle, 1 rad = 57.3 o Angular velocity Define an angular velocity as the rate of change of an angle units are radians/second who has the larger angular velocity, the boy or the girl? boy girl Angular acceleration Define an angular acceleration as the rate of change of the angular velocity units are radians/second 2
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2 Example 9.1 - Rotation of a compact disk A CD rotates at high speed. The disk has radius 6.0cm and while data is being read by the laser it spins at 7200rev/min. What is the CD’s angular velocity in radians per second. How much time is required for it to rotate through 90 o ? If it starts from rest and reaches full speed in 4.0s, what is its average angular acceleration? Directions Rotation can be clockwise or counterclockwise - our sign definition is Constant angular acceleration Equations describing this are analogous to those for constant linear acceleration applying these formulae to rotational problems is just the same as we did previously for translational problems Example 9.2 - Rotation of a bicycle wheel Angular velocity of the rear wheel of an exercise bike is 4.00rad/s at t =0 and it has constant angular acceleration of 2.00rad/s 2 . One of the spokes lies parallel with the x -axis at t =0, what angle does this spoke make with the x -axis at t =3.00s. What is the wheel’s angular velocity at this time? one full rotation is rad
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3 Tangential acceleration Recall that when we considered uniform circular motion we required a constant radial acceleration to keep the speed constant but change the direction if the rotational speed changes, this requires we have a nonzero tangential acceleration to change the speed but not the direction Throwing a discus
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This note was uploaded on 04/09/2008 for the course PHYS 111n taught by Professor Sukenik during the Spring '08 term at Old Dominion.

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Chapters 9 & 10 - Rotation and angles Chapters 9 and...

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