Rotational Motion Chapter 7 Rotational Motion Motion about an axis of rotation. A record turntable rotates; A bug sitting on the record revolves around.
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Slide 1
Slide 2
Rotational Motion Chapter 7
Slide 3
Rotational Motion Motion about an axis of rotation. A record
turntable rotates; A bug sitting on the record revolves around the
axis and is said to undergo circular motion.
Slide 4
Particles in the rings of Saturn rotate using circular
motion.
Slide 5
Spin cycle of washer The spin cycle of your washer works on the
principle that your clothing is forced to follow a circular path,
but the water in the clothing escapes through holes in the side of
the drum, not following a circular path.
Slide 6
Measuring rotational motion: You have probably already
encountered the radian, the measure of angular displacement: Angle
whose arc length = its radius = s/r is anglular in radians, s is
arc length, r is radius Converting to degrees: 2 (rad) = 360
(deg)
Slide 7
Just like linear displacement, the direction matters.
Conventionally, rotation is.. Positive when Counterclockwise
Negative when Clockwise Lets do the problem on P246. H/W P247
Q1-4
Slide 8
P247 answers 1. 1.7 rad 2.Pi rad, 1.2 m 3. 0.34 rad 4.2.5
rad,6.4m, - 320 , 1.1m
Slide 9
Angular velocity: Think of it as how quickly something is
turning A unit that is often used is revolutions per minute (RPM)
Old records spun at 33.3, 45 or 76 RPM Car engines often run most
efficiently at about 2500 RPM and produce the maximum power about
4500rpm Most electric motors spin at a multiple or sub multiple of
3600RPM or 60 revolutions/sec
Slide 10
Angular velocity (speed) Just like motion in a straight line,
after displacement comes speed . Angular speed is the rate of
change of angular displacement = /t Units are rad/s Lets do problem
on P248 H/W P248 Q1-4
Slide 11
P248 answers 1.29 rad/s 2.2.2 rad/s 3.7.3 X 10- 5 rad/s 4.A)
0.23 rad/s b) 0.24 rad c) -6.3 rad/s d) 0.75s
Slide 12
Angular acceleration: Think of it as how quickly a rotating
object speeds up or slows down. The angular acceleration of the
earth is High:Low: Zero The angular acceleration of a bicycle wheel
is pulling away from a stop High:Low:Zero The angular acceleration
of a motorcycle doing a constant 150mphis High:Low:Zero The angular
acceleration of a motorbike wheel pulling away from a race start is
High:Low: Zero
Slide 13
Angular acceleration Rate of change of angular velocity, = f i
t Units are rad/s 2 Lets do Problem on P249 H/W P. 250 Q1,2,3
Angular kinematic equations: f = i + t = i t + 1/2 t 2 f 2 = i
2 + 2 ( f - i ) =1/2 ( i + f ) t
Slide 16
Answers to P 252 9.0 rad/s 25 rad/s 2 15 rad/s 31 rad/s 0.89
rad/s
Slide 17
Section review: 1.0.44rad, 0.61 rad, 2.23 rad, 4.7 rad 2.-1.0
rad 3.0.314 rad/s 4.0.20 rad/s 2 5. 0.70 rad/s Page 269 Q10:
0.042rad/s, Q11a) 821rad/s 2, b) 4.2 X10 3 rad
Slide 18
Remember the strategy: Write down the givens and unknown. Find
the equation that has all the givens and unknown and nothing else.
If necessary, rearrange the equation to find the unknown and then
substitute to solve.
Slide 19
Tangential Speed (7.2) Speed of an object (m/s) traveling in a
circle is called Tangential Speed because the direction of motion
is always in a tangent to the circle.
Slide 20
Tangential speed: Tangential speed would be important to find
out how fast a point on the earth is travelling in a given time etc
v t (m/s) = r
Slide 21
Tangential Acceleration: The rate of change of tangential
speed. It is the linear acceleration of a point undergoing angular
acceleration: a t (m/s 2 ) = r
Slide 22
Centripetal acceleration: Acceleration directed toward the
center of a circle that an object undergoing circular motion must
experience. (Note spinning cup with water in it) a c = v t 2 / r a
c = r 2
Slide 23
H/W : P255 1-4, P256 1-3, P258 1-5 P250 1.8m/s 6.9 m/s 9.2 m/s
3.6 m/s, 15 rad/s, 29m/s, 1.3m P256: 2.11 m/s 2, 0.18m/s 2, 1.0m/s
2
Centripetal force: In order for an object to travel in a
circle, something must provide a force that is directed at all
times toward the center of the circle. This force is called
CENTRIPETAL FORCE. For a car going around the corner, the force is
provided by the ______. For a stone being twirled in a slingshot it
is provided by the _______. For clothes in the spin cycle it is
provided by______
Slide 26
For the moon traveling around the earth it is provided by
_______. For the earth traveling around the sun it is provided by
_______. Can you think of any other objects that undergo circular
motion and identify what provides the centripetal force?
Slide 27
Demonstration The object on the left travels with inertia,
while the object on the right is caused to travel in a circle by
the wooden block. Centripetal force is applied.
Slide 28
Calculating Centripetal Force
Slide 29
Inertia should cause the car to continue in the direction in
which it was traveling. What causes it to travel in a circular
direction? What applies the centripetal force?
Slide 30
If you let go, youll be like Mary Poppins and fly off the
Merry- go-Round.
Slide 31
You do not fly straight outward. Instead you follow tangential
motion, and continue in a straight line from the point where the
circular motion ends.
Slide 32
As usual, there is a formula: (From F=ma) F c = mv t 2 / r F c
= mr 2 Homework: P261 Q1-5
Slide 33
Newtons universal law of gravitation There is an attractive
force between any two masses or particles in the universe F = - G m
1 m 2 r 2 Where G is the universal gravitational constant, m is
each mass in kg, and r is the distance separating their centers of
mass G = 6.67 X 10 -11 N m 2 / kg 2
Slide 34
P265 1-3 top of page And Section review Keep in mind that, for
an orbiting body, centripetal force = gravitational force.
Slide 35
Speed of an orbiting satellite: V s = (G M c /r) 1/2 Where M c
is central mass, r is the total distance from center of
rotation.
Slide 36
Escape Velocity: There is a speed at which an object shot
straight up from a planet will have enough energy to escape the
gravitational field of the planet. V esc = ( 2MG/R) 1/2 M is the
mass of the planet.
Slide 37
g, the acceleration due to gravity on any planet surface : g =
G M p / r p 2
Slide 38
Homework: Find your gravitational force on the earths surface
using universal G formula. (1lb = 0.45kg) Compare with the weight
formula result. Compare with your gravitational force in orbit
300km above the earths surface. Find g for each planet and the
moon. Find the escape velocity for each planet and the moon.
Slide 39
Rotational Speed (angular speed) The number of rotations/unit
of time. RPM = rotations/min
Slide 40
Centripetal Force Centripetal force is a force that causes an
object to travel in a circle.
Slide 41
How does mass impact Centripetal Force
Slide 42
Centrifugal Force Centrifugal means Center-fleeing and it is a
force that seems to push you outward. Think playground Merry-go-
Round
Slide 43
What it really is is inertia. Newtons First Law applies
always.
Slide 44
Inertia, Centrifugal Force In a car.
Slide 45
Kids, Dont try this at home Experts state that you can swing a
bucket of water over your head and it wont fall out because of
centrifugal force (INERTIA). What they dont say is that when you
stop swinging, it will drench you!
Slide 46
The breaking string revisited What kind of tension would be in
that string?
Slide 47
In action
Slide 48
Rotational Mechanics Torque Rotational analog of Force;
Produces rotation More leverage = More Torque
Slide 49
Torque changes the rotational motion of an object.
Slide 50
What is Torque?? Used when you use a hammer claw to remove a
nail Used when you use a long- handled wrench to loosen a bolt The
longer the handle, the greater the torque
Slide 51
Important facts to increase Torque The force must be applied
perpendicular to the plane. The Longer the Lever, the greater the
force.
Slide 52
Formula Torque = force (perpendicular) x Lever Arm
Slide 53
Look at the pictures on page 151. How does having the doorknob
in the center of the door impact the torque?
Slide 54
See-Saw Torque When a large child and a small child play on the
same see- saw, how do they balance the torques?
Slide 55
Triple Beam Balances Triple Beam Balances work the same way as
the see-saw. You slide the weights on the arms to balance the
torques. The same mass moved farther down the arm produces more
torque.
Slide 56
Rotational motion and torque in an auto engine.
http://science.howstuffworks.com/fpte4.htm
Slide 57
Torque Diagram
Slide 58
Torque measurement Torque = Force x lever arm
Slide 59
Torque & Center of Gravity Stand with your back and heels
against the wall. Then try to lean forward to touch your toes. What
happens to you??
Slide 60
You now have your center of gravity located somewhere other
than over your feet, so you
Slide 61
See the sketches on page 154. If you kick a football at its
center of gravity, what happens? If you kick a football above or
below its center of gravity, what happens?
Slide 62
Rotational Inertia Just like in the inertia as learned before
An object that is rotating about its axis will continue to rotate
about its axis. Rotational inertia depends on the mass of the
object and the distribution of mass relative to the axis of
rotation. The more mass and the further it is on average from the
axis, the higher the moment of inertia.
Slide 63
See P285 (P262 Hons)
Slide 64
Moment of inertia for rotating objects is analogous to mass for
objects in linear motion. Which will roll down a hill first, a
basketball or a bowling ball? A tire or a wheel/tire assembly? A
solid golf ball or a hollow lead sphere? A tennis ball or a
ping-pong ball?
Slide 65
Angular momentum: Just like momentum (P = m v) for objects
moving in a straight line Angular momentum, L = I , where L is the
angular momentum, I is the moment of inertia and is angular speed.
Angular momentum is conserved if there is no net external
torque.
Newtons second law for rotation Ch 9:4 hons. Before we had F =
ma Can you think of what the rotational equivalent might be? Net
external orque = I X Where I is the moment of inertia and is
angular acceleration.
Slide 70
Rotation and energy, Ch 9:5 hons. Before we had work = F x d
What do you think the rotational equivalent of work might be?
Kinetic energy = I x 2 Work (Joules) = Net external Torque x
Homework : P156: Q13, 15, 18. P 281:28, 29, 31 and P282 Q43, 44,
45, 46
Slide 71
Baseball and torque Why does a batter choke up on the bat? Page
155
Slide 72
Formulas for rotational inertia See page 157 of the text
book.
Slide 73
Which will roll down the slope faster? See page 158. The hoop
will roll faster that has the least inertia. Why?
Slide 74
Gymnastics and Inertia What are the three principal axes of
rotation of the human body? (page 159) Each axis has a different
rotational inertia.
Slide 75
Angular Momentum Angular momentum is a vector quantity And the
momentum is conserved. A gyroscope swivels around, but the spin
stays the same. See page 161
Slide 76
See page 162 How does angular momentum impact the balance of a
bicycle rider?
Slide 77
Conservation of Angular Momentum Law of Conservation of Angular
Momentum states: If no unbalanced external torque acts on a
rotating system, the angular momentum of that system is
constant.
Slide 78
Read page 163. How does that apply to figure skating?
Slide 79
Why does a cat land on its feet (usually) when it falls? Page
163
Slide 80
Space and Angular Momentum Read the box on page 163. How does
angular momentum relate to the shape and speed of rotation of a
galaxy?