Transcript CP Physics Chapter 7

CP Physics Chapter 7
Angular Motion
s
 
r
180 deg =  rad
1 rot = 2  rad
1 rev = 2  rad
Example #1
What is the arc length traveled by an
object moving 158 degrees if it is
located 3.3 m from the center of
revolution?
Example #2
Convert the following to radian:
A. 30 deg
B. 129 deg
C. 0.38 rev
D. 333 deg
E. 2.5 rot
F. 7 rev
Convert the following to degrees:
A. 1.3 rad
B. 3.8 rad
Angular Displacement and
Velocity


t
Example #3
What is the angular displacement of a rotating
tire with a diameter of 37 cm that spins 30 times
a second?
What is the total distance traveled by the rim of
the tire?
Angular Velocity?
Example #4
A child is riding on a merry-go-round. How
far from the center is she if she travels a
total distance of 55.6 m and makes 4
complete revolutions?
If it took her 1 min to make 4 revs, what is
her angular velocity?
Rotational Big 4
Linear Motion
v f  vi  at
Rotational Motion
i   f  t
1 2
d  at  vi t
2
v 2f  vi2  2ad
1 2
  t  i t
2
 2f  i2  2
1
d  (vi  v f )t
2
1
  (i   f )t
2
Example #5
A 37 cm diameter tire starts from rest and
rotates to 10 rotations per sec in 3 sec.
A.What is the angular acceleration?
B. How many radians did the tire rotate
through?
C. How many rotations?
Example #6
A wheel rotates from rest to 15 rad/sec in 2-sec.
A)What is its angular acceleration?
B)
How many rotations in that time?
Example #7
A dryer starts from rest and rotates 2 times
until it reaches full speed of 1.5 rot/sec.
A.What is the angular acceleration?
B. How long will it take to do this?
Tangential Velocity and
Acceleration
vt = r
at = r
Tangential Cat
Example #8
Tangential Cat is attached to a spinning
fan traveling at 1.8 m/sec. If the cat is
0.8 m from the center of the fan, what
is the cat’s angular speed?
Example #9
A dog on a merry-go-round undergoes
1.5 m/sec2 which is 1.0 rad/sec2. How
far from the center is the dog?
Example #10
My father was a world known fast pitch
softball pitcher who used the slingshot
technique. Upon the end of his backswing, his
0.66 m arm is at rest and accelerates for 0.05
sec until he releases the ball. If the ball is
thrown at 31.7 m/sec, what is the angular
speed of his arm upon release of the ball, the
at, and the angular displacement?
Centripetal vs. Centrifugal
Acceleration and Force



Inertial vs. Noninertial reference frames
Fc is a net force – not an action/reaction force
Therefore, centrifugal force does not exist!
Centripetal Force




Centripetal means “center-seeking”
It’s the force that holds an object in
its circular path.
The centripetal force is always
directed towards the center of a
rotating object.
Centripetal force is the
TRUE FORCE!
Centrifugal Force





Centrifugal means “center-fleeing”
It’s the “force” that pulls you away from the
center.
It’s the “force” you feel when a car takes a
curve or when you’re spinning on an
amusement park ride.
In reality, if the centripetal force were to
disappear, you would fly off tangent to the
circle because no force was acting on you,
not because the centrifugal “force” pulled you
away.
Centrifugal force is NOT A TRUE FORCE!
Centripetal Acceleration/Force
2
T
v
2
ac 
 r
r
Example #11
A little kid swings a yo-yo around above his head with a centripetal
acceleration of 3.1 m/sec2. If the string is 2.1 m, what is the yoyo’s tangential speed?
Example #12
A piece of clay on a pottery wheel
is about 0.2 m from the axis of
rotation. If the wheel is spinning
at 20.5 rad/sec,
A. what is the centripetal
acceleration of the clay?
B. what is the tangential speed of
the clay?
Example #13
A 0.9 kg mass is tied to the end of a 1.2 m string
and whirled above your head 4 times every second.
What is the centripetal force exerted on the mass?
Example #14
A 0.9-kg mass is tied to the end
of a 1.2-m string and whirled
vertically 4 times every second.
A)What is the tension of the
string at the top of the path?
B) At the bottom of the
path?
Example #15
The Steel Force at Dorney Park has a radius of curvature
of 42 m at the bottom of the first hill and travels at 32
m/sec.
A)
What do you weigh at the bottom of that hill?
B)
What is your force factor?
42 m
Example #16
At the top of the camelbacks riders experience a force
factor of -1. If the train is moving at approximately 10
m/sec, what is the radius of curvature of the track?
R=?
Example #17
A car rounds a curve with a 50
m radius of curvature. If the
coefficient of friction between
the tires and road is 0.9, how
fast can the car go without
skidding?
Example #18
Riding the nauseating ride called the ROTOR.
This ride has a radius of 2.1 m. The coefficient of
friction between the wall and you is about 0.6.
How fast must that cylinder rotate in order for you
to stay “plastered”
to the wall?
Bobsled Banking
Newton’s Universal Law of Gravitation
Gm1m2
F
2
r
6.67  10
11
Nm2
2
kg
Example #19
What is the attractive force between a 1
kg object and the Earth?
Example #20
Two guys are standing 0.5 m apart. Their
masses are 80 kg and 95 kg. What is their
attraction to each other?