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:
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 (password protected)
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. Wind turbines, rotational motion
Chapter 2.1
Wind turbines, rotational motion
Demos and Objects
Concepts
Wind turbines (rotating wheel)
Opening rusty screws
rotating objects
pirouettes
levers
angular displacement
angular velocity
angular acceleration
moment of inertia (rotational mass)
Torque
Newton’s I. & II. law for rotational motion
levers
mechanical advantage

4. Windturbines Observations about wind turbines:
(this chapter is more about rotational motion than wind turbines, generators to create electricity come later)
Observations about wind turbines:
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 that’s rotating tends to continue rotating.
Demonstration: Spin a Balanced Object on a Pivot
Demonstration: Orient Balanced Object at Various Angles
We ignore friction for the time being

7. Physical Quantities for rotational motion
Angular Position – an object’s 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 earth’s motion around its own axis?
1 Year
1 Day
1 revolution/year
1 revolution/day

12. Newton’s First Law of Rotational Motion
A rigid object that’s 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 that’s 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 object’s mass balances
A free object rotates about its center of mass while its center of mass follows the path of a falling object
Demo: Spin an object on the table and see about which point it spins.

15. Where is the center of mass of these objects?

16. We have to apply a torque to it
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. Moment of inertia (rotational mass)
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 object’s rotational inertia, its resistance to change in angular velocity
Analogous to mass (translational inertia)
Demos: rotating two sticks with different mass distribution
Rotate other objects
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??

21. Physical Quantities Angular Position – an object’s 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. Torque = Moment of Inertia · Angular Acceleration
Newton’s Second Law of Rotational Motion
The torque exerted on an object is equal to the product of that object’s 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 object’s angular acceleration.

24. Mechanical advantage A 200 N child can support a 400 N child
How does a crowbar work?
How does a bottle opener work? F1 r2 r1 F2
Your bottle opener has a total length of 10 cm and the opening hook is at 1 cm. You apply a force of 10 N, what force is applied to the lid?
i-clicker-5
1 N
10 N
11 N
100 N
110 N

25. F2 r2 F1 r1

26. Angular position (angle): q
Summary: Angular and linear quantities
Linear motion
Rotational motion
Position: x
Angular position (angle): q
Angular velocity: w
Velocity: v
Angular Acceleration: a
Acceleration: a
Torque:
Force:
Newton 2
Newton 2
Rotational mass: I
Mass: m