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2012_1061_Lecture_Ch_10

# 2012_1061_Lecture_Ch_10 - Rotation Motion Chapter 10...

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Rotation Motion Chapter 10

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Angular Quantities Wheel rotating counter clockwise – Each point P moves in a circular path by an angle theta l is the length P travels as the wheel rotates through the angle theta – Make sure to use radians when calculating not degrees.
In three dimensions •Note the difference between the position of the point P and the distance of the point to the axis of rotation. •Points at different z position can have the same distance with respect to the axis of rotation

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Angular displacement (rad) Average angular velocity (rad/s) Instantaneous angular velocity (rad/s) To describe a rotational motion we make use of angular quantities .

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Average angular acceleration (rad/s 2 ) Instantaneous acceleration (rad/s 2 ) Converting to the linear variables
Angular and Tangential Accelerations

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Defining the direction of the angular velocity and angular acceleration
Vector Nature of Angular Quantities Linear velocity is a vector Angular velocity is a pseudovector

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Constant Angular Acceleration Angular Linear
Centrifuge acceleration A centrifuge rotor is accelerated from rest to 20,000 rpm in 30 s. – a ) What is its average angular acceleration? – b) Through how many revolutions has the centrifuge rotor turned during its acceleration period, assuming constant acceleration a) The initial angular velocity is ,the final angular velocity is: b) Then since and

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Centrifuge Acceleration b) To find the angular displacement we can use We convert into revolutions
Torque (dynamics of rotation) For rotation we require a force applied at some distance from the axis of rotation (lever arm)

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Force times the distance from its line of action to the axis of rotation defines the torque

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Torque on a compound wheel Two thin disk-shaped wheels, of radii R A = 30 cm and R B =50 cm are attached to each other on an axle that passes through the center of each. Calculate the net torque on this compound wheel due to the two forces shown, each of magnitude 50 N.
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2012_1061_Lecture_Ch_10 - Rotation Motion Chapter 10...

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