Download Circular motion key p. 18 to 22

Circular Motion
Q
Physical Model
m
Object (mass = m) is rotating in a circle
(radius = r) at the end of a string with a
constant angular velocity
tanqential velocity (vt) - speed of an object along a line drawn tangent to its circular path
Note: the magnitude of vt is constant, but the direction is always changing.
of the circular motion) is required for this
Acceleration (directed toward the ÿÿ
change in direction...
Centripetal acceleration (ac) Note: centripetal means " ÿeÿ- ÿeeÿ/ÿ ÿr'ÿe_
oo=d
Period (T) - the time (s) it takes for an object to go around one complete revolution.
Vt :
ac I
ÿ .ÿ
Newton's 2nd Law applies lÿ,
/./7/zÿ/.7- L
Fnet = ma
Since there is an acceleration, there must be a force...
Centripetal Force, Fc - moves an object and holds it in its circular path.
Fc : mac = m (vt2 / r)
OR
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Fc = mac = m (4sÿr / T2)
Iillustrations of centripetal force:
A string exerting tension on a twirling ball horizontally,
/.-" .............. ÿ,
it
Example: A ball with a mass of 0.300 kg is twirled on the end of a
string in a horizontal circle of radius 1.20 m. It takes 20.4 s to
complete 10 revolutions. Find the period of the motion, the tangential
velocity, the centripetal acceleration, and the tension in the string.
.
,
"-.
,,
/'
Can a body move in a circular path without being accelerated? Why or why not?
,do.
vÿloc,'ÿd ;'ÿ a. veÿ"? ÿ, d;'ÿ4,ÿ'ÿ" wÿ" ;'ÿ'; ÿ"+-'ÿ"'
r
2. What is the centripetal acceleration of a locomotive that travels around a circular curve
of radius 250 m at a constant speed of 70. kin/h? (1.5 m/s2)
¢1ÿ ÿ......ÿ-
"c
ÿ
-
70 O0Oÿk
hr
3b oo.ÿ
c1',ÿ = 7
,
What is the centripetal acceleration of a small girl standing at the outer edge of a
carousel 4.0 m in diameter, which makes one complete rotation in 6.0 s? (2.2 m/sz)
z/71 zr--
qC- 7
d
oI:4
7"-
19
A 1200 kg car whose velocity is 6.0 m/s rounds a turn whose radius is 30. m. What is the
,
centripetal orce on the car? (1440 N)
F--
12oÿ x Gÿ
50ÿ
3o
lqo?
5. If the car in problem 4 question rounds the same turn at 12 m/s, the required centripetal
force is
m VÿZ
a. halved
I ÿ ÿiIZ)'ÿ
ÿ -
b. the same
iÿ
,ÿ
c. doubled
"
quadrupled
/ ÿfÿO ÿJ
6. The maximum centripetal force that friction can provide the above car on a rainy day is
8000 N. What is the highest velocity at which the in Problem 4 and 5 can enter the turn
and still "hold the road"? (14.1 m/s)
F
171€ ,,/{
Oÿ
U'= 50 'ÿ
7. What is the direction of the force acting on clothes in the spin cycle of a washing
machine?
o
/1,re4 ÿ-ÿ,ÿ Lÿ tLoujocrÿ eÿ--ÿ);,ÿ' eÿo't % ÿoÿlJ "ÿ1ÿ, oaJ
If you whirl a tin can on the end of a string and the string suddenly breaks, the can will
a. fly directly away from you
b. fly directly toward you
(ÿfly off, tangent to its circular path.
d. spiral away from your hand
2o
,
Practice Day Problems
A lasso is whirled so that the loop at its end describes a horizontal circle with a radius of
5 m. If each revolution of the lasso requires 4 seconds, find the centripetal acceleration
of the loop. (12.3 m/sz)
C
7
2. Which has greater tangential speed, a horse near ÿe outside kalÿlÿof a merry-go-round or
a horse near the inside rail?
J
,
A 0.02-kg ball is whirled in a horizontal circle at the end of a string 0.5 m long whose
tension is 1 N. Neglecting gravity, what velocity does the ball have? (5 m/s)
Oooÿlÿj
O, O'Z---
21
4. A 4 kg rock is spun in a circle with a radius of .5 meters. It takes .2 seconds for the rock
b.
How much tension is there in the string? (remember, tension = Fc) 7897 N
--1,4ÿ_.. ÿ_ # )<' Iq7¢ "= 72¢7 M
5. An 1800 kg car whose velocity is 15 m/s rounds a turn whose radius is 60 m.
a. What is the centripetal acceleration of the car? (3.75 m/s2)
b0
What is the centripetal force acting on the car? (6750 N)
ICe."= "ÿc
f!'o--<,> x 5,,.7d-
U T[o /U
c.ÿ = 5< "2g-ÿ.. ÿ
.
Two objects sit on a table. One has a mass of 3 kg and the other 6 kg. They are 5
meters apart. What is the gravitational attraction between them? 4.8 x 10 -11 N
Tÿ
7
6 . g.(7 ÿ<.:j:'N ' ÿ
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