Rotational Motion

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Rotational Motion

• AP Physics C

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Introduction

• The motion of a rigid body (an object with a
  definite shape that does not change) can be
  analyzed as the translational motion of its
  center of mass AND the rotational motion about
  its center of mass.
• All points on a rotating rigid body move in
  circles and the center of these circles lie on a
  line called the axis of rotation

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Axis of Rotation
Axis of Rotation
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Angular Displacement

• Angular Displacement
• Symbol ?
• Unit radian, rad
• 360 2p radians
• 1 rad 57.3

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Angular Velocity

• Angular Velocity
• Symbol ?
• Unit rad/s
• Direction use RHR
• Every point on a rotating rigid body has the same
  ?

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Angular Acceleration

• Angular Acceleration
• Symbol a
• Unit rad/s2
• Direction See figure
• Every point on a rotating rigid body has the same
  a

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Angular Acceleration
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Angular Linear Analogies

• ??
• ?
• a

• ?x
• v
• a

In rotational motion if you know the analogous
quantity in the linear realm all you do is
replace the linear quantity with the angular
quantity and you have the angular equation
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Relating Angular to Linear
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Moment of Inertia aka Rotational Inertia

• The tendency of a body to resist a rotation

Unit kgm2
See board for derivation
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Rotational Kinetic Energy
This is not a new form of energy, rather it is
the sum of the individual kinetic energies of the
individual particles of the rigid body written in
a compact and convenient form.
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Energy is still conserved
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Parallel Axis Theorem
The moment of inertia for an axis through the
center of mass is lower than for any parallel axis
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Moment of Inertia with Calculus
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Rotational Dynamics What causes rotational
motion?

• An applied force causes motion therefore an
  applied force is necessary to make a body rotate
  but where that force is applied will also
  determine the rotation of the body

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Torque

• The quantitative measure of the tendency of a
  force to cause or change the rotational motion of
  a body.
• Angular force

Direction use RHR Unit m N
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Magnitude of Torque lever arm vs F-
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Rotational analogy for Newtons 2nd Law (rigid
bodies only)
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Work and Power in Rotational Motion
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Angular Momentum
Unit kgm2/s
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Newtons 2nd Laws Rotational Analog in terms of
angular momentum