Physics 101 Chapter 8 Rotation

8/12/2019 Physics 101 Chapter 8 Rotation

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2010 Pearson Education, Inc. Fig. 5-CO, p.76


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2010 Pearson Education, Inc.


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Chapter 8:

ROTATIONAL MOTION


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Circular Motion

When an object turns about an internal

axis, it is undergoing circular motion or

rotation. Circular Motion is characterized by two

kinds of speeds:

tangential(or linear) speed. rotational(or circular) speed.


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Tangential Speed

The distancetraveled by a point on the rotating objectdivided by the time taken to travel that distance is called itstangential speed (symbol v)

Points closer to the circumference have a highertangentialspeedthan points closer to the center.

Fig. 8.1


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8/52 2010 Pearson Education, Inc.

A ladybug sits halfway between the rotational axis and the outer

edge of the turntable . When the turntable has a rotationalspeed of 20 RPM and the bug has a tangential speed of 2 cm/s,what will be the rotational and tangential speeds of her friendwho sits at the outer edge?

A. 1 cm/s B. 2 cm/s C. 4 cm/s D. 8 cm/s

Rotational and Tangential Speed

CHECK YOUR NEIGHBOR



A ladybug sits halfway between the rotational axis and the

outer edge of the turntable . When the turntable has arotational speed of 20 RPM and the bug has a tangentialspeed of 2 cm/s, what will be the rotational and tangentialspeeds of her friend who sits at the outer edge?

A. 1 cm/sB. 2 cm/s

C. 4 cm/s

D. 8 cm/s

Rotational and Tangential Speed

CHECK YOUR ANSWER

Explanation:

Tangential speed =

Rotational speed of both bugs is the same, so

if radial distance doubles, tangential speed

also doubles.So, tangential speed is 2 cm/s 2 = 4 cm/s.

r

Can we make this

compl icated?!!!



Rotational Inertia

An object rotating about an axis tends to

remain rotating about the same axis at the

same rotational speed unless interfered

with by some external influence.

The propertyof an object to resist changes

in its rotational state of motion is called

rotational inertia (symbol I).



Rotational Inertia

Depends upon

massof object.

distribution of mass around axis of

rotation.

The greater the distance

between an objects mass

concentration and the axis, the

greater the rotational inertia.

Fig. 8.9



Rotational Inertia

The greater the rotational inertia, the harder it is

to change its rotational state. A tightrope walker carries a long pole that has a high rotational

inertia, so it does not easily rotate.

Keeps the tightrope walker stable.

Fig. 8.10


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Rotational Inertia

Depends upon the axis aroundwhich it rotates

Easier to rotate pencil around an

axis passing through it.

Harder to rotate it around verticalaxis passing through center.

Hardest to rotate it around vertical

axis passing through the end.

Fig. 8.11


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Rotational Inertia

The rotational inertia depends upon the shape of theobject and its rotational axis.

Fig. 8.15


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A hoop and a disk are released from the top of an

incline at the same time. Which one will reach thebottom first?

A. Hoop

B. DiskC. Both together

D. Not enough information

Rotational Inertia

CHECK YOUR NEIGHBOR

Fig. 8.14


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Torque

The tendency of a force to cause rotation is called

torque. Torque depends upon three factors:

Magnitude of the force

The direction in which it acts

The point at which it is applied on the object

Fig. 8.16


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Torque lever arm force

Torque

The equation for Torque is

The lever arm depends upon

where the force is applied.

The direction in which it acts.


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TorqueExample

1stpicture: Lever arm is lessthanlength of handle

because of direction of force. 2nd picture: Lever arm is equalto length of handle.

3rdpicture: Lever arm is longerthan length ofhandle.

Fig. 8.20


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Torque

Clockwise Torque = Counterclockwise Torque

Fig. 8.18


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Center of Mass and Center of Gravity

Center of mass (CM)is the averageposition of all the mass that makes up the

object.

Center of gravity (CG) is the averageposition of weight distribution.

Since weight and mass are proportional,

center of gravity and center of mass usually

refer to the same point of an object.


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Fig. 8.22


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To determine the center of gravity

Of a regular object,move fingers from ends toward center of

object (Fig. 8.25)



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Of an irregular object suspend the object from a point and draw a vertical line

from suspension point.

repeat after suspending from another point.

The center of gravity lies where the two linesintersect.

Fig. 8.28


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The center of mass of a non-vertically or

non-horizontally thrown or fired objectfollows aparabolictrajectory.

Fig. 8.21


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Center of gravity(mass) may lie outside of an

objects mass

Fig. 8.27

Fig. 8.28

Fig. 8.31

Fig. 8.32


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Center of GravityStability

The location of the center of gravity

is important for stability.

If we draw a line straight down from the

center of gravity and it falls insidethe

base of the object, it is in stable

equi l ibr ium; it will balance.

If it falls outside the base, it is unstable.

Fig. 8.29


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An object with a wide base and low center of

gravity is more stable.

Fig. 8.36


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Centripetal Force

Any force directed towarda fixed centeris called a

centr ipetalforce. Centripetal means center-seeking or toward the

center.

Examples of the centripetal force

Ball on a string Car in a curve

Space shuttle in orbit

Amusement park rotor ride

Note: Something must provide the centripetal force for

an object to travel in a circle!


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Centripetal Force


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When a car rounds a

curve, the centripetal force

prevents it from skidding

off the road.

If the road is wet, or if thecar is going too fast, the

centripetal force is

insufficient to prevent

skidding off the road.


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Centripetal Force


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Suppose you take a sharper turn than before and

halvethe radius, by what factor will the centripetalforce need to change to prevent skidding?

A. Double

B. Four timesC. Half

D. One-quarter

Centripetal Force

CHECK YOUR NEIGHBOR

Centripetal Force


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Suppose you take a sharper turn than before and

halvethe radius, by what factor will the centripetalforce need to change to prevent skidding?

A. Double


D. One-quarter

Centripetal Force

CHECK YOUR NEIGHBOR


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Lift force on the wings provides

the centripetal forceto keep the

airplane flying in a loop

Centripetal acceleration may

be several times as great as g,so pilot may experience forces

several times greater than his

weight (g forces)


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2010 Pearson Education, Inc. Fig. 8.41

A l M


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Angular Momentum

Theinertiaof rotation of rotating objects is called

angu lar m omentum. This is analogous to inertia of motion, which was

momentum.

Linear momentum mass velocity (Chapter 6)

Linear momentum = mv

Angular momentum rotational inertia angular velocity

Angular momentum = I

=mvr


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C ti f A l M t


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Conservation of Angular Momentum

An external net torque is required to change the angular

momentum of an object.

Rotational version of Newtons first law: m1v1= m2v2 (Ch. 6)

The law of conservation of angular momentum states:

If no external net torqueacts on a rotating system, the

angular momentum of that system remains constant.

m1v1r1 = m2v2r2

Angular Momentum


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Suppose you are swirling a can around and suddenly

decide to pull the rope in halfway; by what factor wouldthe speed of the can change?

A. Double


D. One-quarter

g

CHECK YOUR NEIGHBOR

Angular Momentum


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Suppose you are swirling a can around and suddenly

decide to pull the rope in halfway; by what factor wouldthe speed of the can change?

A. Double


D. One-quarter

g

CHECK YOUR NEIGHBOR


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Angular Momentum


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Suppose by pulling the weights inward, the rotational

inertia of the man reduces to half its value. By whatfactor would his angular velocity change?

A. Double

B. Three timesC. Half

D. One-quarter

g

CHECK YOUR NEIGHBOR


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Fig. 8.53


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Physics 101 Chapter 8 Rotation

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