Main
Kinematical Quantities
- Introductory concepts: Axis of rotation; Expressing angles
in radians.
- Angular displacement:
  = 2 – 1,
usually measured in radians in this chapter.
- Frequency: The rate at which the number of turns changes
in time, f = n / t.
- Angular velocity: The rate at which changes
in time,
 =
limit of / t for
small t.
- Angular acceleration. The rate at which changes,
 =
limit
of / t for
small t.
- Relationship with linear motion: d = r,
v = r,
at = r,
aR = 2r or
v2/r.
Rotational Dynamics
- Torque: The torque of a force F applied a distance r from
an axis is
 =
rF sin.
- Moment of inertia: For an extended object, use a table; For
a composite object, add all the individual moments of inertia; For
a particle,
I = mr2 .
- Newton's 2nd law for rotations: Relation torque-angular acceleration, net =
I .
- Rotational kinetic energy: KErot =
I2 /
2. This kinetic energy is used when rotation is involved, in the same
equations as the translational kinetic energy, for example the conservation
of energy equation.
- Angular momentum: L = I;
When is the angular momentum of a system conserved?
Examples and Problems
- Rolling motion: Be able to apply the no-slipping
condition
v = r to
a problem.
- Problem solving: Be able to apply Newton's second law (for
translation and for rotation), or conservation of energy, or conservation
of angular momentum, as appropriate to each problem.
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