Chapter 2: The laws of motion, Part IIFirst 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

- Homework 1.3 due Tuesday, Feb. 2

- Web page for class is: http://www.wfu.edu/~gutholdm/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 (password protected)

Announcements:

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)

Chapter 2.1 Wind turbines, rotational motion

- 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

Demos and Objects Concepts

• 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

Windturbines(this chapter is more about rotational motion than wind turbines,

generators to create electricity come later)

Observations about wind turbines:

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?

A.Yes, she still spins (slower).

B.No, she will stop spinning.

C.Not enough information.

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.

We ignore friction for the time being

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)

Angular rotation or

Angular position,

• SI unit of angular rotation is the radian

• One radian is 180°/57.3°

• Rotation requires an axis of rotation

Angular velocity

• 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

Angular velocity is a vector

Right-hand rule for determining the direction of this vector.

• rotates through the same angle,

• has the same angular velocity,

• has the same angular acceleration.

Every particle (of a rigid object):

i-clicker-2

What is the angular velocity of earth’s motion around its own axis?

A.1 YearB.1 DayC.1 revolution/yearD.1 revolution/dayE.0

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.

When an object is rotating freely (no fixed axis), it rotates about its center of mass

Center of mass

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

Where is the center of mass of these objects?

B

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

FrLever arm is perpendicular to applied force(non-perpendicular force will produce smaller torque)

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,

- Index finger is lever, r

- Middle finger is Force, F

i-clicker-4

What is the net torque the mechanics is applying to the screw?

A.500 Nm

B.0.5 m

C.250 Nm

D.250 N

E.90 N

F

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°.

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)• 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

i-clicker: Which object is hardest to rotate??

A.

B.

C.

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

Newton’s Second Lawof 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

I

Physics Concept

• Net Torque– The sum of all torques

on an object.– Determines that object’s

angular acceleration.

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

A. 1 NB. 10 NC. 11 ND. 100 NE. 110 N

F2

r2

F1r1

Summary: Angular and linear quantities

I

Angular position (angle):

Torque:

Linear motion Rotational motion

maF

Position: x

Force:

Velocity: v Angular velocity:

Acceleration: a Angular Acceleration:

Mass: m Rotational mass: I

Newton 2 Newton 2