Motion
Introduction
The language of kinematics lets us describe motion -- and changes
in motion -- with precision. But what causes motion to change?
Isaac Newton provided the answer in the 1600's, when he stated
that that the acceleration of an object is equal to the sum of
the forces on it, divided by its mass.
We now refer to this as Newton's Second Law. The study of forces
and their effects on motion is called dynamics.
Mass
The mass of an object is a measure of the amount of matter in an object. Mass is reported in either kilograms (SI units) or slugs (English units). Every object has a mass. This mass remains constant unless additional masses (other objects) are added to it. For example, a skater's mass increases when he or she puts on his or her skating boots. Once the skater is on the ice performing, his or her mass is constant. The mass of an object is also a measure of the amount of inertia the object possesses. For example, the more massive a skater the more inertia he or she has. In practical terms this means that it takes more force for a larger, more massive skater to get moving than for a smaller, less massive skater.
Weight
The term weight is often confused with that of mass. The weight of an object is proportional to its mass. The proportionality constant, g, has the dimensions of an acceleration: W=mg.
On the earth's surface, the above values are referred to as
the gravitational acceleration. This value is constant near the
earth's surface. In other words, we use weight to represent the
mass of the object times the acceleration due to gravity (W =
mg). The units of weight are newtons (SI units) or pounds (English
units). Weight is a vector, having both magnitude and direction.
The direction of the weight of an object is always toward the
center of the earth (straight down).
Center of Gravity
The center of mass is the balance point of a system, a point where you could consider the mass of the whole system to be concentrated. In a system which has moveable joints, i.e. the system can move or be moved into different configurations or positions, the location of the center of mass depends on the position of the system. For example, when a figure skater lifts his or her arms during a spin, the mass of the arms is higher up in the system than when the arms were at the side of the skater. With more mass of the skater distributed in a higher position in the body, the center of mass of the skater rises to a higher position in the body.
Momentum
Angular momentum is a measure of the tendency of an object to keep rotating, or moving in a circle. Angular momentum depends on both the rotational inertia of an object and the angular velocity of the object. For example, a small skater spinning with arms tight against the body will be easier to stop then a large skater spinning with arms spread wide, assuming that they are both spinning at the same speed. Angular momentum equals the rotational inertia of an object times the angular velocity.
Linear Momentum is the tendency of an object to keep moving. Momentum is a vector quantity and depends on both the mass of the object and the velocity of the object. For example, two skaters of the same mass, but skating at different speeds, have different momentum. The faster skater has more momentum than the slower skater. A consequence of this is that the skater going faster will have to exert more force to stop than the skater going slower. Momentum is equal to:
Velocity
Velocity is a measure of both the speed and direction that an object is traveling. Technically it is the time rate of change of displacement. Average velocity is calculated by dividing displacement by time. Velocity is measured in meters/second (SI units) or feet/second (English units).
Do not forget that when using velocity, the direction of motion is as important as the speed of the object.
Measurement of linear velocity
Angular velocity is the time rate of change of angular
displacement. More simply it is a measure of how fast an object
is rotating. For example, the measure of a skater's spinning speed
during a sit spin is called angular velocity. Angular velocity
is calculated by subtracting the initial angular position from
the final angular position and dividing by the time it took to
get from the initial to final position. Angular velocity is measured
in radians/second (SI units) or degrees/second or revolutions/second
(English units).
Inertia
A term which describes the resistance of an object to change
in velocity. The greater the inertia, the more resistant the object
is to either an increase or decrease in velocity. In other words,
it would take more force to change the velocity of an object which
has greater inertia.
Moment of Inertia
Moment of inertia, also called rotational inertia, is a measure of an object's resistance to rotation. It is analogous to inertia, an object's resistance to change in linear velocity. The rotational inertia of an object depends on the mass of the object, the shape of the object, and how the mass is distributed throughout the object's shape.
The most common example, which would be easier for you to demonstrate
in class, is swinging a baseball bat from the handle end and the
barrel end. A baseball bat is much easier to swing (rotates easier)
when swung from the barrel end. This is because more of the mass
of the bat is located closer to the axis of rotation -- your hands.
The farther away the mass of an object is from the axis of rotation,
the harder it is to swing the object, and the greater the rotational
inertia.
Linear Acceleration
Acceleration is a measure of the time rate of change of velocity.
Acceleration can be caused by a change in speed or direction or
both. For example, a skater who goes from a standstill to full
speed quicker than another skater has greater acceleration. Likewise,
a skater who can stop quicker than another skater has greater
deceleration--assuming both skaters were traveling at the same
speed. Another example of acceleration is a skater who travels
at a constant speed around the ice rink. In the corners, when
this skater is changing direction, and thus has a changing velocity,
he or she has acceleration. Acceleration is calculated by subtracting
the starting velocity of an object from the final velocity, and
dividing by the time between this change in velocity.
