Transcript Circular Motion

Evaluate, measure, and analyze circular motion.
Analyze and evaluate the nature of centripetal forces.
Investigate, evaluate and analyze the relationship among
centripetal force, centripetal acceleration, mass, velocity,
radius.
Carousal
 Carousels are as reliant on the laws of
motion as their more exciting cousins,
the roller coasters.
 It's theoretically possible that, allowed
to spin out of control, a carousel could
gain enough speed so that the riders
would be thrown off.
Carousal Continued…
 With all of its beauty and seeming simplicity, the
carousel is a delicate balance of motion and forces.
 All of the horses move through one complete circle in the
same amount of time.
 The horses on the outside of the carousel have to cover
more distance than the inside horses in the same amount
of time.
 This means the horses on the outside have a faster linear
speed than those at the hub.
Carousal (galloping horses)
 On some carousels, the horses go up and down in a
galloping motion simulating what it might be like to ride
a real horse.
 In a normal carousel, each horse maintains a constant
acceleration, radius, and tangential speed (speed tangent
to the circular path of the carousel).
 If you add a gallop to some of the horses, you must
consider the forces needed to change that horse's position
upward or downward as it goes around the track.
 In designing with these forces in mind, you also need to
take into account the mass of the horse and its rider.
Carousal (Lead Horse)
 How do you tell the lead horse on a carousel?
 According to carousel legend, the lead horse of any
carousel is always the biggest, most decorative horse.
 In many instances, this horse is a military or war horse.
 If a chariot is included in the carousel, the first horse right
behind the chariot on the outside is the lead horse.
Circular Motion
 Kinematic concepts and motion principles will be applied
to the motion of objects in circles and then extended to
analyze the motion of such objects as roller coaster cars,
a football player making a circular turn, and a planet
orbiting the sun.
Uniform Circular Motion
 The motion of an object in a circle with a constant or
uniform speed.
 If you were driving a car at a constant speed and you
were following the path of a perfect circle you would be
experiencing uniform circular motion.
 An object moving in uniform circular motion would
cover the same linear distance in each second of time.
Circular Motion
 The equation suggests that for objects moving around
circles of different radius in the same period, the object
traversing the circle of larger radius must be traveling
with the greatest speed.
 In fact, the average speed and the radius of the circle are
directly proportional.
Circular Motion
 A twofold increase in radius corresponds to a twofold
increase in speed; a threefold increase in radius
corresponds to a three--fold increase in speed; and so on.
Circular Motion
- If Uniform Motion means constant speed, does that also
mean that it has constant velocity?
- Remember that velocity is a vector quantity as speed is a
scalar quantity.
- A vector quantity has both magnitude and direction.
- The magnitude of velocity is simply the instantaneous
speed of the object.
- The direction is directed in the same direction which the
objects moves.
Circular Motion
 Since an object is moving in a circle, its direction is
continuously changing.
 The best word that can be used to describe the direction
of the velocity vector is the word tangential.
Circular Motion
 Does an object traveling in uniform circular motion have
acceleration?
 Acceleration, like velocity, is a vector quantity and has
both magnitude and direction.
 The magnitude is the change in speed over a given time.
 The direction will go in the direction of the object, just as it
did with velocity.
 A change in either the magnitude or the direction
constitutes a change in the velocity.
Circular Motion (calculating
A)
Circular Motion (Candle Demo)
 The flame deflects from its upright position, which
signifies that there is an acceleration when the flame
moves in a circular path at constant speed.
 A careful examination of the flame reveals that the flame
will point towards the center of the circle, thus
indicating that not only is there an acceleration; but that
there is an inward acceleration.
 Objects moving in a circle at a constant speed experience
an acceleration which is directed towards the center of
the circle.
Circular Motion
Which of the following shows acceleration?
a.
b.
c.
d.
e.
Circular Motion (test knowledge)
Explain the connection between your answers to the above
questions and the reasoning used to explain why an object
moving in a circle at constant speed can be said to experience
an acceleration.
Dizzy Smith and Hector Vector are still discussing #1e. Dizzy
says that the ball is not accelerating because its velocity is not
changing. Hector says that since the ball has changed its
direction, there is an acceleration. Who do you agree with?
Argue a position by explaining the discrepancy in the other
student's argument.
Identify the three controls on an automobile which allow the car
to be accelerated.
An object is moving in a clockwise direction around a circle at
constant speed. Use your understanding of the concepts of
velocity and acceleration to answer the next four questions. Use
the diagram shown at the right.
Which vector below represents the direction of the velocity vector
when the object is located at point B on the circle?
Which vector below represents the direction of the acceleration
vector when the object is located at point C on the circle?
Which vector below represents the direction of the velocity vector
when the object is located at point C on the circle?
Which vector below represents the direction of the acceleration
vector when the object is located at point A on the circle?
Centripetal Force
 Law of Inertia (Newton’s 1st Law)
 "... objects in motion tend to stay in motion with the same
speed and the same direction unless acted upon by an
unbalanced force.“
 Objects will tend to naturally travel in straight lines; an
unbalanced force is required to cause it to turn.
 The presence of the unbalanced force is required for
objects to move in circles.
 During the turn, the car travels in a circular-type path;
that is, the car sweeps out one- quarter of a circle.
 The unbalanced force acting upon the turned wheels of
the car cause an unbalanced force upon the car and a
subsequent acceleration.
 The unbalanced force and the acceleration are both
directed towards the center of the circle about which the
car is turning.
 Your body however is in motion and tends to stay in
motion. It is the inertia of your body - the tendency to
resist acceleration
 This phenomenon might cause you to think that you
were being accelerated outwards away from the center
of the circle.
 You are merely experiencing the tendency of your body
to continue in its path tangent to the circular path along
which the car is turning.
Centripetal Force
 Any object moving in a circle (or along a circular path)
experiences a centripetal force.
 The word centripetal is merely an adjective used to
describe the direction of the force.
 We are not introducing a new type of force but rather
describing the direction of the net force acting upon the
object which moves in the circle.
Examples of Centripetal
Force
As a car makes a
turn, the force of
friction acting upon
the turned wheels of
the car provides
centripetal force
required for circular
motion.
As a bucket of water
is tied to a string and
spun in a circle, the
tension force acting
upon the bucket
provides the
centripetal force
required for circular
motion.
As the moon orbits
the Earth, the force
of gravity acting
upon the moon
provides the
centripetal force
required for circular
motion.
 An object is moving in a clockwise direction around a circle at
constant speed. Use your understanding of the concepts of velocity,
acceleration and force to answer the next five questions. Use the
diagram shown at the right. Click the button to check your answers.
Which vector below represents the direction of the force vector when
the object is located at point A on the circle?
Which vector below represents the direction of the force vector when
the object is located at point C on the circle?
Which vector below represents the direction of the velocity vector
when the object is located at point B on the circle?
Which vector below represents the direction of the velocity vector
when the object is located at point C on the circle?
Which vector below represents the direction of the acceleration vector
when the object is located at point B on the circle?