Class 26 Rotation

1
Class 26 - Rotation Chapter 10 - Monday October
25th

• Review
• Kinetic energy, moment of inertia, parallel axis
  theorem
• Newton's second law for rotation
• Work, power and rotational kinetic energy
• Sample problems

Reading pages 241 thru 263 (chapter 10) in
HRW Read and understand the sample
problems Assigned problems from chapter 10 (due
Sunday October 31st at 11pm) 2, 10, 28,
30, 36, 44, 48, 54, 58, 64, 78, 124
2
Kinetic energy of rotation
Parallel axis theorem

• If moment of inertia is known about an axis
  though the center of mass (c.o.m.), then the
  moment of inertia about any parallel axis is

• It is essential that these axes are parallel as
  you can see from table 10-2, the moments of
  inertia can be different for different axes.

3
Some rotational inertia
4
Torque

• The ability to rotate an object about an axis
  depends not only on the force you apply, but also
  where and in what direction you apply the force.
• In particular, the further away from the axis
  that you push, the easier it is to rotate the
  object.

5
Torque

• There are two ways to compute torque

• The direction of the force vector is called the
  line of action, and r? is called the moment arm.

6
Torque

• Torque is actually a vector quantity given by the
  following vector product

• Thus, torques add like vectors, i.e. if several
  torques act on an object, the net torque tnet is
  given by the vector sum.

• In this chapter, you will not need to worry about
  the vector character of t, since we shall only
  consider rotational motion about a fixed axis.

7
Newton's second law for rotation

• We can relate Ft to the tangential acceleration
  using Newton's second law

For a rigid body which is free to rotate about a
fixed axis, Fr cannot affect the motion.
8
Work and rotational kinetic energy

• By now, you should be noticing a pattern in the
  connections between linear and angular equations
  x ? q v ? w a ? a m ? I F ? t, etc..

9
Summarizing relations for translational and
rotational motion

• Note work obtained by multiplying torque by an
  angle - a dimensionless quantity. Thus, torque
  and work have the same dimensions, but you see
  that they are quite different.