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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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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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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.



θ (rad) =

θ (deg)

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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°

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Angular speed describes

The rate at which a body

Rotates about an axis, usually

Expressed in rad/s.



ω =

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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.



α =

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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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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


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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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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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

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Newton’s 2nd Law for

Rotating objects.

τ = Iα

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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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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


Fb = 16 N Fa = 41 N

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The centrifugal force is an

Apparent force.


It is not a real force because there

Is no physical outward push.

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The Coriolis Force is also a


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.