ch. 5 circular motion ppt

7/25/2019 Ch. 5 Circular Motion PPT

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Circular Motion

Physics Grade X

Physics Grade X Immanuel Christian School Senior High [Bilingual Class]

Devilim, S.Si.

After studying this topic, you are expected to be able to:

describe qualitatively motion along circular path as

due to a perpendicular force which causes a

centripetal acceleration

express angular displacement in radians

solve problem using the concept of angular velocity

recall and use equation for centripetal acceleration

(a = v2/r, a = rw2)

recall and use equation for centripetal force (F =

mrw2, F = mv2/r)


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Devilim, S.Si.

Circular Motion

Velocity magnitude + direction

Magnitude changed acceleration

Direction changed?

There is acceleration!

Example?

Revolution of earth around sun Solar system


Devilim, S.Si.

Why it moves in circle? Move in circle there is acceleration there is

force towards the center of circle

Acceleration to the center of circle

= centripetal acceleration

Centripetal acceleration (ac) :

Force to center of circle = centripetal force

(fc):

F = m.ac.


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Devilim, S.Si.

Example:

Wall of Death


Devilim, S.Si.

Question:

Red book p. 133 B no. 5

Red book p. 132 A no. 7

Red book p. 134 C no. 3


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Devilim, S.Si.

A certain light truck can go around a flat curve having

a radius of 150 m with a maximum speed of 32.0 m/s.

With what maximum speed can it go around a curve

having a radius of 75.0 m?

A certain light truck can go around a flat curve having

a radius of 250 m with a maximum speed of 50.0 m/s.

With what maximum speed can it go around a curve

having a radius of 80.0 m?


Devilim, S.Si.

A 40.0-kg ice-skater is moving at 4.00 m/s when she

grabs the loose end of a rope, the opposite end of

which is tied to a pole. She then moves in a circle of

radius 0.800 m around the pole. Determine the force

exerted by the horizontal rope on her arms.

A 50.0-kg ice-skater is moving at 5.00 m/s when she

grabs the loose end of a rope, the opposite end of

which is tied to a pole. She then moves in a circle of

radius 0.500 m around the pole. Determine the force

exerted by the horizontal rope on her arms.


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Devilim, S.Si.

How to Deal with Circular Motion?

Quantities of Circular Motion

Radian (unit for measuring angles)

1 full circle = 360o

length (1 circle) = 2pr

360o = 2p rad

unit of : radian rad


Devilim, S.Si.

Frequency & Period

frequency = how many full circles in 1 second

f = total circle/time

period = how many seconds to move 1 full

circle

T = total time/how many circlerpm (rotations orrevolutions per minute)

Rpm = how many circles in 1 minute

From rpm to frequency?

From frequency to rpm?


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Devilim, S.Si.

Exercise 1

Convert the unit

1. 75o = . Rad

2. 570o = . Rad

3. (2p/5) rad = . o

4. 30 rad = . o

Find , f, T

5. Travel 120o in 2

seconds

6. Travel 400o in 5 second

7. Has 240 rpm

8. Has 1200 rpm


Devilim, S.Si.

Angular Displacement (q)

How much angle turned

Unit: radians (rad)

:

Length : .


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Angular Velocity (w)

How much angle turned over time

Unit: radians/second (rad/s)

2

Or

2 : .


Devilim, S.Si.

Try it

Find q, w, f, rpm, v, s, ac Going 6 turns in 5 seconds, 2 meters from

the centre of the circle

Having period of 10 seconds and diameter

of 10 meter, travels for 2 minutes Travels 300o in 50 second, 10 cm from the

centre of circle


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Devilim, S.Si.

Angular Acceleration (a)

Change of angular velocity (w) over time

Unit: radians/second2 (rad/s2)

Because : .

/

. : .


Devilim, S.Si.

Compare circular and linear motion

Circular motion Linear motion

q s = r . q

w v = r . w

aa = r .

a

In this case, a is not centripetal acceleration,

but is called tangential acceleration

(acceleration with same direction as its linear

velocity)


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Devilim, S.Si.

Compare circular and linear motion

Circular motion Linear motion

. . .

12 .

. 12 .

2. .

2 . .

Motion with constant acceleration


Devilim, S.Si.

QUIZFor no. 1 until 4, find its q, w, f, rpm, v, s, ac.

1. Going 540o in 4 seconds, radius 5 m

2. Going 1000o in 2 minutes, radius 10 m

3. Going 10 turns in 10 minutes, diameter 6 m

4. Going 20 turns in 10 seconds, diameter 10 m

5. Have frequency of 1/50 Hz and radius of 1 m, find its w, v, andrpm

6. Have frequency of 1/25 Hz and radius of 4 m, find its w, v, and

rpm

7. A tire with diameter of 1 m rotates 500 rpm for 5 minutes.

Find its q, w, v, total distance travelled, and ac.

8. A tire with diameter of 2 m rotates 400 rpm for 5 minutes.

Find its q, w, v, total distance travelled, and ac.


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Applications of Circular Motion

Gears

Road Reaction

Roller coaster

Banked road


Devilim, S.Si.

GEARS3 types of gears

relationships:

r1

r2

r1

r2

r1

r2


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Devilim, S.Si.

GEARS CONNECTION

How are the ws and the vs?

r1

r2

r1

r2

r1

r2

Same centre

Same w

Not-

connected

edge

Different v

Different centre

Different w

Connected edge

Same v

Different centre

Different w

Connected edge (use

string)

Same v


Devilim, S.Si.

Road Reaction

On top of the hill:

.

. .

If N1 0 (no contact with road, you feel

like flying), then:

. .

When passing through a dip:

.

. .

The difference (N2 mg) provides the

centripetal force


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Devilim, S.Si.

Roller Coaster

Same concept with road reaction


Devilim, S.Si.

Banked Roadon flat road:

Fc car friction between tires and the

road.

Car crash if it exceeds limiting

friction cant travel fast

on banked road:

Fc car provided by N on the car.

Certain speed: no sideways friction

in the tires.

vertically: . cos . horizontally: . s i n . combined together, it becomes:

t a n

.


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Devilim, S.Si.

A stone is tied to a string and then rotated horizontally at

an angular velocity of 200 rpm. If the length of the string

is 10 cm, calculate:

a) the frequency of motion of stone

b) the period of motion of the stone

c) the angular speed of the stone (in rad/s)

d) the linear speed of the stone


Devilim, S.Si.

At an airshow, an 2000-kg aircraft is moving in

circular path of diameter 500 m at a constant speed of

1000 m/s. Calculate:

a.its angular velocity

b.its centripetal acceleration

c.its centripetal force


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Devilim, S.Si.

The figure shows a cylinder of radius 0.7 m

rotating about its axis at 10 rad/s. Calculate the

speed of point P.


Devilim, S.Si.

Look at the following figure. It is known that

diameter of gear A is 4 times diameter of gear B.

If diameter of A is 20 cm, and gear A rotates with

constant angular speed of 10 rad/s, calculate:

a. linear speed of Ab. angular speed of B

BA


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Devilim, S.Si.

Suppose that a 2000-kg car passes over a bump

in a roadway that follows the arc of a circle ofradius 20 m, as in Figure below.

(a)What force does the road exert on the car as

the car passes the highest point of the bump if

the car travels at 9 m/s?

(b)What is the maximum speed the car can have

without losing contact with the road as it

passes this highest point?


Devilim, S.Si.


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Devilim, S.Si.


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Devilim, S.Si.

A flywheel rotating at 12 rpm is brought to rest

in 6 seconds. Calculate the magnitude of

angular acceleration of the flywheel.





Devilim, S.Si.

An airplane propeller slows from an initial angular

speed of 12 rev/s to a final angular speed of 5

rev/s. During this process, the propeller rotates

through 20 revolutions. Find the angular

acceleration of the propeller in radian/second2,

assuming its constant.


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Devilim, S.Si.

In a compact disc player, as the read head moves out

from the center of the disc, the angular speed of the disc

changes so that the linear speed at the position of the

head remains at a constant value of about 2 m/s.

(a) Find the angular speed of the compact disc when the

read head is at r = 2.0 cm and again at r = 5.6 cm.

(b) An old- fashioned record player rotates at a constant

angular speed, so the linear speed of the record

groove moving under the detector (the stylus)

changes. Find the linear speed of a 45.0-rpm record

at points 2.0 and 5.6 cm from the center.(c) In both the CD and phonograph record, information is

recorded in a continuous spiral track. Calculate the

total length of the track for a CD designed to play for

1.0 h.


Devilim, S.Si.




A flywheel rotating at 20 rpm is brought to restin 5 seconds. Calculate the magnitude of



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Devilim, S.Si.

A compact disc rotates from rest up to an angularspeed of 30 rad/s in a time of 0.8 s.

(a)What is the angular acceleration of the disc,

assuming the angular acceleration is uniform?

(b)Through what angle does the disc turn while

coming up to speed?

(c)If the radius of the disc is 4 cm, find the final

tangential speed of a microbe riding on the rim

of the disc.

(d)What is the magnitude of the tangential

acceleration of the microbe at the given time?

ch. 5 circular motion ppt

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