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Chapter 8 Rotational Motion

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Chapter 8 Rotational Motion - PowerPoint PPT Presentation


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8.1 Describing Rotational Motion. When an object spins, It is said to undergo Rotational motion. . When measuring rotational Motion, we will use radians.. A radian is an angle whose Arc length is equal to its radius,Which is approximately Equal to 57.3?. ? = . sr. . ? = the angle. r = the rad

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slide1
Chapter 8

Rotational Motion

slide2
8.1 Describing Rotational Motion

When an object spins,

It is said to undergo

Rotational motion.

slide3
When measuring rotational

Motion, we will use radians.

A radian is an angle whose

Arc length is equal to its radius,

Which is approximately

Equal to 57.3°

slide4
s

r

θ =

θ = the angle

r = the radius

s = arc length

slide5
360° = 2π rad

We now have a conversion

Between radians and degrees.

π

180°

θ (rad) =

θ (deg)

slide6
Problem...

Ben, riding on a carousel,

Travels through an arc length of11.5 m. If the carousel has a

Radius of 8 m, what is the angular

Displacement? What degree is this?

2.88 rad 165°

slide7
Angular speed describes

The rate at which a body

Rotates about an axis, usually

Expressed in rad/s.

Δθ

Δt

ω =

slide8
Problem...

Ben now spins on a stool, if he

Turns clockwise through 10π rad,

During a 10 s interval, what is

The average angular speed

Of his feet?

3.14 rad/s

slide9
Angular acceleration is the time

Rate of change of angular speed,

Usually expressed in radians

Per second per second.

Δω

Δt

α =

slide10
Problem...

Now Ben rotates on the stool

With an initial angular speed of

21.5 rad/s. The stool accelerates,

And after 3.5s, the speed is 28

rad/s. What is the average

Angular acceleration?

1.9 rad/s/s

slide12
Problem...

The wheel on an upside-down bike

Rotates with a constant angular

Acceleration of 3.5 rad/s/s. If the

Initial angular speed of the wheel

Is 2 rad/s, through what angular

Displacement does the wheel

Rotate in 2 sec?

11 rad

slide13
8.2 Rotational Dynamics

Torque is a quantity that measures

The ability of a force to rotate

An object around some axis

slide14
Torque is a scalar quantity.

Torque has the SI unit of

N*m

τ = Fd(sinθ)

slide15
Torque is positive or negative

Depending on the direction

The force tends to rotate

An object.

Torque that is clockwise is

Defined as negative.

Thus torques that produce a

Counterclockwise rotation are

Defined to be positive.

slide16
Problem...

Find the torque produced by a

3 N force applied at an angle

Of 60° to a door 0.25m from

The hinge.

0.65 N m

slide17
In order to calculate the moment

Of inertia, you have to use the

Formulas provided in the book

For the many different shapes.

slide19
Problem...

A 5m horizontal beam weighing

315N is attached to a wall so

That it rotates. Its far end is

Supported by a cable at an angle

Of 53°, and a 545N is standing

1.5m from the wall. Find the tension

And the force on the beam by the

Wall, R.

Tension = 403 N R = 590N

slide20
Newton’s 2nd Law for

Rotating objects.

τ = Iα

slide21
Problem...

A catapult propels a 0.150 kg

Stone. The length of the

Catapult arm is 0.350m. If the

Stone leaves the catapult with an

Acceleration of 100 m/s2, what

Is the torque exerted on the stone.

5.25 Nm

slide22
8.3 Equilibrium

The center of mass of an object

Is the point at which all the

Mass of the body can be

Considered to be concentrated

When analyzing

Translational motion.

slide23
Rotational and translational

Motion can be combined.

The moment of inertia is the

Rotational analog of mass.

Equilibrium requires zero net force,

And zero net torque.

slide24
Problem...

A 5.8 kg ladder, 1.8 m long, rests

On 2 saw horses. Sawhorse A is

0.6 m from one end of the ladder

And sawhorse B is 0.15 m from the

Other end of the ladder. What force

Does each sawhorse exert on the

Ladder?

Fb = 16 N Fa = 41 N

slide25
The centrifugal force is an

Apparent force.

NOT A REAL FORCE!

It is not a real force because there

Is no physical outward push.

slide26
The Coriolis Force is also a

FAKE FORCE!

This is because it is only apparent

To rotating observer.

This is very apparent on Earth

However. It is the reason for

The direction of the winds.

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