Announcements

1

• Announcements
• Midterm 2 on Wednesday, Oct. 19.
• Material Chapters 7-11
• Review on Tuesday (outside of class time)
• Ill post practice tests on Web
• You are allowed a 3x5 inch cheat card
• Go through practice exams homework class
  examples understand concepts demos
• Time limit for test 50 minutes

2
Conservation of energy (including rotational
energy)
Again If there are no non-conservative forces
Energy is conserved. Rotational kinetic energy
must be included in energy considerations!
3
Black board example 11.5
Connected cylinders.

• Two masses m1 (5 kg) and m2 (10 kg) are hanging
  from a pulley of mass M (3 kg) and radius R (0.1
  m), as shown. There is no slip between the rope
  and the pulleys.
• What will happen when the masses are released?

1. Find the velocity of the masses after they have
   fallen a distance of 0.5 m.
2. What is the angular velocity of the pulley at
   that moment?

4
Torque
f
A force F is acting at an angle f on a lever that
is rotating around a pivot point. r is the
______________ between F and the pivot point.
This __________________ pair results in a torque
t on the lever
5
Black board example 11.6
Two mechanics are trying to open a rusty screw on
a ship with a big ol wrench. One pulls at the
end of the wrench (r 1 m) with a force F 500
N at an angle F1 80 the other pulls at the
middle of wrench with the same force and at an
angle F2 90 .
What is the net torque the two mechanics are
applying to the screw?
6
Torque t and angular acceleration a. Newtons
__________ law for rotation.
Particle of mass m rotating in a circle with
radius r. force Fr to keep
particle on circular path.
force Ft accelerates particle along tangent.
Torque acting on particle is ________________ to
angular acceleration a
7
Definition of work
Work in linear motion
Component of force F along displacement s. Angle
g between F and s.
Work in rotational motion
Torque t and angular displacement q.
8
Work and Energy in rotational motion
Remember work-kinetic energy theorem for linear
motion
External work done on an object changes its
__________ energy
There is an equivalent work-rotational kinetic
energy theorem
External, rotational work done on an object
changes its _______________energy
9
Linear motion with constant linear acceleration,
a.
Rotational motion with constant rotational
acceleration, a.
10
Summary Angular and linear quantities
Linear motion
Rotational motion
Kinetic Energy
Kinetic Energy
Torque
Force
Momentum
Angular Momentum
Work
Work
11
Rolling motion
Pure rolling There is no ___________
Linear speed of center of mass
12
Rolling motion
The _______ __________ of any point on the wheel
is the same.
The linear speed of any point on the object
changes as shown in the diagram!! For one instant
(bottom), point P has _______ linear speed. For
one instant (top), point P has a linear speed of
____________
13
Rolling motion of a particle on a
wheel (Superposition of ________ and ___________
motion)
Rolling


Rotation
Linear
14
Rolling motion
Superposition principle Rolling motion
Pure _________ Pure _______
Kinetic energy of rolling motion
15
Chapter 11 Angular Momentum part 1
Reading assignment Chapter 11.4-11.6 Homework
(due Monday, Oct. 17, 2005) Problems 30, 41,
42, 44, 48, 53

• Torque
• Angular momentum
• Angular momentum is conserved

16
Torque and the ______________
Thus far Torque
Torque is the _____________ between the force
vector F and vector r
17
Torque and the vector product
Definition of vector product
f

• - The vector product of vectors A and B is the
  ___________.
• C is _________________ to A and B
• The __________________ of is C ABsinf

18
Torque and the vector product
f

• Use the right hand rule to figure out the
  direction of C.
• __________ is C (or torque t, angular velocity
  w, angular momentum L)
• _____________ finger is A (or radius r)
• ____________ finger is B (or force F)

19
Torque and the vector product
f
Rules for the vector product.
1. 2. 3. 4. 5. Magnitude of C ABsinq is
equal to area of ______________ made by A and B
If A is ______ to B then . Thus,
If A is _______ to B then
20
Torque and the vector product
f
Rules for the vector product (cont).
6.
21
Black board example 12.2 HW 21
A force F (2.00i 3.00j) is applied to an
object that is pivoted about a fixed axis aligned
along the z-axis. The force is applied at the
point r (4.00i 5.00j).

1. What is the torque exerted on the object?
2. What is the magnitude and direction of the torque
   vector t.
3. What is the angle between the directions of F and
   r?