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Lecture

SCI206 Lecture Notes - Moment Of Inertia, Tennis Ball, Figure Skating

3 pages66 viewsSummer 2011

Department
Science
Course Code
SCI206
Professor
Andrew Morton

Page:
of 3
Topic 1
Thursday, October 05, 2006
1:56 PM
Topic 1: Motion
From Lecture
Newton's Laws
What are the 3 ways to describe motion?
o Position, velocity, and acceleration
How can we describe position?
o We use a vector, because it can tell us direction and distance (from some defined start
point)
What are the 2 parts of velocity?
o How fast we are going (speed)
o What direction we are going in (direction)
What is acceleration?
o It is how fast (and in what manner) our velocity is changing
What is Newton's first law?
o An object that is not subject to any net outside forces moves at constant velocity
What is Newton's second law?
o The force exerted on an object is equal to the product of the object's mass times its
acceleration
o The acceleration is in the same direction as the force
What is Newton's third law?
o For every force that one object exerts on a second object, there is an equal but
oppositely directed force that the second object exerts on the first object
Gravity and Componential Motion
What is gravity? What determines the effect we will experience due to gravity?
o It is a downward force produced by the earth which acts on us, pulling us down
o The gravitational effect we experience is always an acceleration of ~10 m/s2 --
REGARDLESS of our mass
This means that (neglecting air resistance) a feather falls just as fast as a brick
Why doesn't gravity cause us to fall through the floor?
o Because of the "normal force": an upward force produced by the surface we are
standing on that counteracts the gravitational force so that we don't move
Describe the motion of a projectile launched at some angle with respect to the horizontal.
o We can break up its initial velocity into horizontal and velocity components
Its horizontal velocity will never change, because there are no forces present to
change it (recall Newton's First Law)
Its vertical velocity will be subject to gravity, so its upward progress will slow,
eventually become zero, then start to head downwards
If you wanted to shoot a monkey in a tree, where should you aim? (Assume that the monkey will
drop and fall downwards as soon as the shot is fired).
o You should aim straight at the monkey (not above it or below it), because once the
bullet is in the air and the monkey has dropped, both objects are subject to the same
force (only gravity), and so they will meet at some point
Work and Energy
What is the difference between kinetic and potential energy?
o Kinetic energy is the energy of movement: the amount of this one possesses is related
to one's velocity
o Potential energy is stored: the amount of this one possesses is related to its ability to
unleash energy
Discuss energy conversions.
o Energy cannot be created or destroyed, but it can be converted from one form into
another
o The types of conversions which occur and their efficiencies affect the things we see in
the real world
For example, some materials bounce better than others because they do a
better job of converting kinetic energy to elastic potential (while others just
convert kinetic into heat)
Discuss work, in particular the way it is related to potential energy.
o To do work on something is to exert a force on it and cause it to move some distance in
the direction of that force
o Work is related to potential energy because we can give an object potential energy by
doing work on it
For example, lifting a ball from the ground to a table
Friction
Imagine a scenario where (with friction present) you are pushing a block horizontally across the
floor. Describe the different forces acting on the box.
o There is gravity acting downwards, and the normal force acting upwards
o There is the human pushing force acting in the box's forward direction, and friction
acting opposite to that
The pushing force must exceed the frictional force in order for the box to start
moving from rest
Discuss the 2 kinds of friction. What kind of energy is produced by friction?
o Static friction is friction that opposes the initiation of movement
o Kinetic friction is friction that slows down movement which has already started
o The energy lost from friction (remember that we would expect a given amount of
energy produced given the work we put into moving something…so when we have
reduced energy due to friction, where does that energy go?) becomes HEAT
Explain the "spiky" model of friction.
o On a microscopic level, the two interacting surfaces are not smooth but rather have
many small bumps and crevices, almost like interlocking teeth
Thus moving the surfaces across each other requires energy to overcome this
interlocking mechanism
o When starting from rest, more of the "teeth" are "locked together" and thus the
frictional force experienced is greater
o When already moving, there are fewer teeth interlocked and thus the force is smaller
o If you press the two surfaces together (i.e. if the one on top is heavier), again the
"teeth" "interlock" more, and so friction increases (this is why friction is related to the
normal force)
Explain why a tablecloth can be pulled out from beneath a dinner set.
o It is simply a function of the frictional force between the tablecloth and the dinner
plates: can we pull the tablecloth fast enough that it overcomes the frictional force
which is causing the plates to stick to the cloth? If so, the cloth will come right out from
beneath them...
Rotational Motion
Describe the motion of a tennis ball connected to a string being flung around in the head in a
CIRCULAR pattern.
o Its speed is always the same, but its velocity changes since its direction is always
changing
o It has an acceleration that is always the same in magnitude but always changing in
direction (though it is always pointed towards the middle)
The force creating this acceleration (since f = ma) is known as the "centripetal
force", and it is embodied in the tautness of the string
o If at any time in the motion the ball was separated from the string, it would fly off in a
line tangent to the circle (this is why we feel like we're falling out of the car when we go
around curves)
Recall the experiment where a water-filled bucket was rotated vertically in a circle. What
determines whether the water falls out?
o The relevant relationship here is that the centripetal force (discussed earlier) is related
to the velocity of the motion
And the centripetal force is made up of the tension which swinging the bucket
exerts on the arm PLUS the gravitational force - so if the necessary centripetal
force isn't even as much as the gravitational force, then the remainder of the
gravitational force will be used to allow the bucket to spill
Why do figure skaters spin faster when they bring their arms close into their body?
o Because something called angular momentum is conserved, which is a function of
rotational inertia (analogous to mass) and rotational speed (analogous to velocity)
o As long as torque (a force which affects rotational velocity) is not added to or removed
from the system, angular momentum must stay constant - and so if we reduce our
rotational inertia by bringing our weight closer to the axis of rotation, the rotational
velocity must increase to counteract this
Why did Idziak's tricks with the strings and the hourglass work better when the hourglass was
spinning?
o Because the hourglass wants to conserve angular momentum, and it does this by
continuing to spin on the same axis
o If it were to wobble (i.e. become unstable), this would constitute spinning on another
axis and cause angular momentum to not be conserved - thus it tends to not do this
From Textbook
Chapter 1
Chapter 2
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