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## Chapter 2: The laws of motion, Part II

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### Chapter 2: The laws of motion, Part II First two chapters: Introduce the language of physics Subsequent chapters: Explore objects and underlying physical concepts – PowerPoint PPT presentation

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Title: Chapter 2: The laws of motion, Part II

1
Chapter 2 The laws of motion, Part II First two
chapters Introduce the language of
physics Subsequent chapters Explore objects and
underlying physical concepts
Homework 2.1 due Tuesday, Feb. 9 in class
(Jill Bjerke) Exercises 4, 5, 6, 7, 8, 9, 11,
12, 16, 17 Problems 1, 3, 4, 5, 6
2
Announcements
• Homework 1.3 due Tuesday, Feb. 2
• Web page for class is http//www.wfu.edu/gutho
ldm/Physics110/phy110.htm
• Bring i-clicker to class
• You are allowed 30 missed points in the i-clicker
total score ( 160 points)
• Homework solutions are posted on web page

PHYSICS 110 TUTOR SESSIONS (in OLIN 101, class
room) Tutor Jillian Bjerke Maggie
Baldwin Session 1 Mo, 4-6 pm (Jill) Session
2   We, 4-6 pm (Jill) Session 3 Th, 5-7 pm
(Maggie)
3
Chapter 2.1 Wind turbines, rotational motion
Concepts
Demos and Objects
• Wind turbines (rotating wheel)
• Opening rusty screws
• rotating objects
• pirouettes
• levers
• angular displacement
• angular velocity
• angular acceleration
• moment of inertia (rotational mass)
• Torque
• Newtons I. II. law for rotational motion
• levers

4
Windturbines (this chapter is more about
rotational motion than wind turbines, generators
to create electricity come later)
• Wind turbines are symmetrical and balanced
• A balanced wind turbine rotates smoothly
• An unbalanced turbine settles heavy-side down
• Most wind turbines have three blades
• Wind turbines start or stop spinning gradually
• Wind turbines extract energy from the wind and
convert it into electrical energy

5
i-clicker-1
• A diver does a somersault dive (spinning dive).
First, she is tightly tugged in, then extends.
• Is the diver spinning when (right before) she
hits the water?
• Yes, she still spins (slower).
• No, she will stop spinning.
• Not enough information.

6
Physics Concept
• Rotational Inertia
• In the absence of an external net torque,
• A body at rest tends to remain at rest.
• A body thats rotating tends to continue
rotating.

We ignore friction for the time being
7
Physical Quantities for rotational motion
• Angular Position an objects orientation (angle
with respect to reference, i.e. horizontal
• Angular Velocity its change in angular position
with time
• Torque a twist or spin (more later)

8
Angular rotation or Angular position, q
• SI unit of angular rotation is the radian
• One radian is 180/p 57.3
• Rotation requires an axis of rotation

9
Angular velocity w
• SI unit radians per second or just 1/sec
• An other unit rotations per minute (not an SI
unit).
• Measure of how fast an object spins
• Angular velocity is a vector!
• Use right hand rule to determine direction of
vector
• Align right thumb with axis
• Align fingers with rotational movement
• Thumb points into direction of angular velocity
vector

10
Angular velocity is a vector
Right-hand rule for determining the direction of
this vector.
Every particle (of a rigid object)
• rotates through the same angle,
• has the same angular velocity,
• has the same angular acceleration.

11
i-clicker-2
• What is the angular velocity of earths motion
around its own axis?
• 1 Year
• 1 Day
• 1 revolution/year
• 1 revolution/day
• 0

12
Newtons First Law of Rotational Motion
A rigid object thats not wobbling and that is
free of outside torques rotates at a constant
angular velocity.
• Rotational Inertia
• In the absence of external torques,
• A body at rest tends to remain at rest.
• A body thats rotating tends to continue rotating.

13
Center of mass
When an object is rotating freely (no fixed
axis), it rotates about its center of mass
14
Center of Mass
• The point about which an objects mass balances
• A free object rotates about its center of mass
while its center of mass follows the path of a
falling object

15
Where is the center of mass of these objects?
16
How do we start something spinning??? We have to
apply a torque to it
• We need a
• pivot point
• lever arm
• applied force
• Torque force x lever arm

Lever arm is perpendicular to applied
force (non-perpendicular force will produce
smaller torque)
17
Torque is a vector
It has a direction and a magnitude
• Use the right hand rule to figure out the
direction of the torque
• Thumb is torque, t
• Index finger is lever, r
• Middle finger is Force, F

18
i-clicker-4
A mechanic is trying to open a rusty screw on a
ship with a big ol wrench. He pulls at the end
of the wrench (r 0.5 m) with a force F 500 N
at an angle of 90.
F
• What is the net torque the mechanics is applying
to the screw?
• 500 Nm
• 0.5 m
• 250 Nm
• 250 N
• 90 N

19
Some objects are harder to spin than others.
Moment of inertia (rotational mass)
• The moment of inertia or rotational mass is a
measure of an objects rotational inertia, its
resistance to change in angular velocity
• Analogous to mass (translational inertia)
• Moment of inertia depends on
• mass of object
• and mass distribution (where the mass sits with
respect to axis)
• the axis about which the axis rotates

20
i-clicker Which object is hardest to rotate??
A. B. C.
21
Physical Quantities
• Angular Position an objects orientation
• Angular Velocity its change in angular position
with time
• Torque a twist or spin
• Angular Acceleration its change in angular
velocity with time
• Moment of Inertia measure of its rotational
inertia

22
Newtons Second Law of Rotational Motion
The torque exerted on an object is equal to the
product of that objects moment of inertia times
its angular acceleration. The angular
acceleration is in the same direction as the
torque. Torque Moment of Inertia Angular
Acceleration
23
Physics Concept
• Net Torque
• The sum of all torques on an object.
• Determines that objects angular acceleration.

24
• A 200 N child can support a 400 N child
• How does a crowbar work?
• How does a bottle opener work?

25
(No Transcript)
26
Summary Angular and linear quantities
Linear motion
Rotational motion
Angular position (angle) q
Position x
Angular velocity w
Velocity v
Angular Acceleration a
Acceleration a
Torque
Force
Newton 2
Newton 2
Rotational mass I
Mass m