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Chapter 8 Rotational Motion PowerPoint PPT Presentation


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Chapter 8 Rotational Motion. 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°.

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Chapter 8 Rotational Motion

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Chapter 8

Rotational Motion


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8.1 Describing Rotational Motion

When an object spins,

It is said to undergo

Rotational motion.


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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°


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s

r

θ =

θ = the angle

r = the radius

s = arc length


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360° = 2π rad

We now have a conversion

Between radians and degrees.

π

180°

θ (rad) =

θ (deg)


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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 rad165°


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Angular speed describes

The rate at which a body

Rotates about an axis, usually

Expressed in rad/s.

Δθ

Δt

ω =


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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


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Angular acceleration is the time

Rate of change of angular speed,

Usually expressed in radians

Per second per second.

Δω

Δt

α =


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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


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Angular Kinematics


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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


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8.2 Rotational Dynamics

Torque is a quantity that measures

The ability of a force to rotate

An object around some axis


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Torque is a scalar quantity.

Torque has the SI unit of

N*m

τ = Fd(sinθ)


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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.


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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


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In order to calculate the moment

Of inertia, you have to use the

Formulas provided in the book

For the many different shapes.


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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 = 403NR = 590N


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Newton’s 2nd Law for

Rotating objects.

τ = Iα


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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


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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.


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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.


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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 NFa = 41 N


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The centrifugal force is an

Apparent force.

NOT A REAL FORCE!

It is not a real force because there

Is no physical outward push.


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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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THE END


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