Chapter 9 Rotation

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Chapter 9Rotation
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9-1Rotational Kinematics
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Radians
S
r
q
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Angular velocity
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Angular acceleration
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Motion with Constant Angular Acceleration
These expressions are similar to those for motion
with constant linear acceleration
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9-2Rotational Kinetic Energy
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Rotational Kinetic Energy
Kinetic energy of each piece of disc
Note the angular velocity is the same for each
piece of disc
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Rotational Kinetic Energy
Total kinetic energy of rotating disc
Moment of Inertia
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Rotational Kinetic Energy
Total kinetic energy of rotating disc
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9-4Newtons Second Law for Rotation
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2nd Law for Rotation
Apply 2nd Law to net tangential force
It can be re-written as
where t r Ft is called the torque
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Example 9-10 (1)
Find tension in string and the acceleration of
the block I is the moment of inertia of the
pulley of radius R
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Example 9-10 (2)
Newtons 2nd Law
The torque is t RT so the angular
acceleration of the pulley is
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Example 9-10 (3)
Apply the 2nd Law in the vertical direction
But since the string does not slip
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Example 9-10 (4)
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Example 9-10 (5)
With a bit of algebra we get