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# Chapter 8 Rotational Motion - PowerPoint PPT Presentation

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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Rotational Motion

When an object spins,

It is said to undergo

Rotational motion.

A radian is an angle whose

Arc length is equal to its radius,

Which is approximately

Equal to 57.3°

r

θ =

θ = the angle

s = arc length

We now have a conversion

π

180°

θ (deg)

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?

The rate at which a body

Δθ

Δt

ω =

Ben now spins on a stool, if he

During a 10 s interval, what is

The average angular speed

Of his feet?

Rate of change of angular speed,

Per second per second.

Δω

Δt

α =

Now Ben rotates on the stool

With an initial angular speed of

And after 3.5s, the speed is 28

Angular acceleration?

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?

Torque is a quantity that measures

The ability of a force to rotate

An object around some axis

Torque has the SI unit of

N*m

τ = Fd(sinθ)

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.

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

Of inertia, you have to use the

Formulas provided in the book

For the many different shapes.

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

Newton’s 2nd Law for

Rotating objects.

τ = Iα

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

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.

Motion can be combined.

The moment of inertia is the

Rotational analog of mass.

Equilibrium requires zero net force,

And zero net torque.

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

Apparent force.

NOT A REAL FORCE!

It is not a real force because there

Is no physical outward push.

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.