Chapter 4
Motion, Energy, and Gravity
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Description of Motion
Mass and Weight
Newton’s Law of Motion
Newton’s Law of Gravity
Conservation Laws
Preface
So far we have only used our knowledge on how the
celestial bodies are moving in the universe and with respect
to each other to explain what we see in our sky. We have
not discussed the reasons of why the celestial bodies
move the way they do.
For example,
• Why do the planets orbit the Sun in elliptical orbits,
•
What is keeping the planets from running away from the
Sun? Or,
•
Why does the Moon revolve around the Earth while
the Earth-Moon system revolves around the Sun…
Newton’s Laws of Motion and Laws of Gravity
explains why the celestial bodies move the way
they do…and many more things…
Physical Concepts
These are the physical concepts that will be introduced in this chapter…
These concepts are necessary for the understanding of the motion of
celestial bodies.
• Motion
 Linear motion: speed, velocity, and acceleration
 Angular motion: angular speed, angular velocity, and angular
acceleration
• Mass
− Mass
− Weight
• Force and torque
• Momentum
− Linear momentum
− Angular momentum
• Energy – different form of energy
• Conservation Laws
− Conservation of energy
Description of Motion
When we talk about motion, we need to talk about
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Position: the position of an object with respect to a reference
point.
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We specify position in length units, such as [meter], [foot], [kilometer], [light-year], etc.
Velocity: change in position with respect to a reference point in
a given amount of time.
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Velocity is specified in unit of length divided by time, e.g.,
[meter/second], [kilo-meter/hour], etc.
How fast
Direction
Acceleration: change in velocity with respect to a reference
point in a given amount of time.
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Acceleration is specified in unit of velocity divided by time, e.g.,
[meter/second2], [km/s2].
Change in speed
Change in direction.
Description of Motion
Depending on which description is more convenient for the
problem at hand, we can describe motion in terms of
• Linear motion
– when we are describing motion along a straight line,
or,
• Angular motion
– When we talk about motions along a curved path, such as the
rotation of one object around another.
Angular Motion
The motion of a moving object that is changing its direction is described by
angular motion.
 An object moving on a circle with fixed rotation rate has constant angular
velocity (constant degree/sec and direction of rotation).
 An object moving on a circle with fixed rotation rate has non-zero
acceleration. It is changing its direction all the time.
The orbital motion of the Earth
around the Sun is an example of
angular motion…
• the direction of Earth’s orbital
motion is changing constantly (it
reverses direction every 6
months),
• its angular velocity (w.r.t. to the
Sun) is about 360 degrees/365
days, or about 1 degree/day.
Constant Speed Motion on a
Perfect Circle
• Motion of an object in
a circular orbit can be
described in x-y
coordinate system.
• Or, in angular
coordinate system.
Y
V1
V1
V2
V2
X
Examples of Acceleration
• Acceleration: speeding up
• Acceleration is not just
speeding up or slowing down.
When you are changing
direction, you have
acceleration also!
• Deceleration: slowing down,
negative acceleration.
Linear Acceleration
 An object moving along a straight
line with constant speed has
constant velocity and zero
acceleration
 A car that can go from 0 to 60
km/hour (1 km/minute) in 1
minute has a linear acceleration
of 1 km/minute2
 An object falling off the roof (on
Earth) experiences a constant
linear acceleration downward (g
= 9.8 m/sec2). This is how strong
the Earth’s gravitational force is
at the surface of the Earth.
Angular Acceleration
• Motion of an object in a
circular orbit has
constant speed in radial
direction
• But its direction changes
all the time…
– Therefore, it has nonzero acceleration.
Y
V1
V1
V2
V2
X
Mass
When we talk about motion, another important ingredient is the
property of the object in motion: its mass
– Mass is an intrinsic property of matter, which determines how
fast an object can respond to force.
– Your mass is never zero, unless you don’t exist. Or you are not
matter, but energy, such as light (photons).
– Your mass is the same whether your are on Earth, on the Moon,
or during space walk (weight-less environment).
Weight and Mass
In daily life, we usually think of mass as something we can measure with a
bathroom scale, but technically, the scale measures the weight of an object, not the
mass. The distinction between weight and mass rarely matters when we are talking
about objects on Earth, but it is very important in physics and astronomy…
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Mass is the amount of matter in your body.
Weight is the force that’s acting on your mass.
 Your weight depends on your mass AND the force that is acting on you.
 When you measure your weight, you actually measure the force acting on
you, not just the mass.
 On the surface of Earth, the force that is acting on you is the gravitational
force of the Earth.
 You weigh more on Earth than on the Moon, because the gravitational
force of the Earth is stronger than that on the Moon.
 Your are not weightless when you are in free-fall, like when you are doing
space walk. You feel weightless because you cannot feel the gravitational
force acting on you.
Click here to start animation…
Measuring Weight in an
Elevator
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When you stand on a scale,
you are exerting a force (the
gravitational force pulling on
you) on the scale (or the
scale is exerting a force on
you). This force is your
weight.
When the elevator is not
accelerating up or down
(when its stopped or moving
up or down at a constant
speed), it exerts a force on
you that is exactly equal to
the gravitational force. So,
your weight does not change.
When the elevator is
accelerating up (or down), it
exerts more (or less) force on
you. The net force on you
changes. Therefore, your
weight changes.
Free Fall
Orbital motion can be
considered as a free-fall also…
– If you step off a tall tower, you
will land at a point directly
underneath. While you are
falling, you will feel weightless,
just like when you are orbiting
the Earth in space.
– If you run and jump off the
tower, then you land a point
away from the base of the
tower.
– If you launch yourself on a
rocket horizontally, with just
the right speed, you will be
free-falling forever: you are in
orbit!
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × m × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
Can you take our bathroom spring scales to the Moon and
measure how much you weigh?
a. Yes.
b. No.
Answer
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × cm × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
If you weigh 50 kg (kilo-gram) on Earth, what would your
bathroom spring scale read on the Moon?
~8 kg
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × cm × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
What do you do to make the bathroom spring scale give correct
mass on the Moon?
a. Divide the reading by 6.
b. Multiply the reading by 6.
c. Divide the reading by 9.8
d. Multiple the reading by 9.8
Answer
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × cm × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
Can you take a balance scale to the Moon and measure how
much you weigh?
a. Yes.
b. No.
 Answer
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × cm × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
r
Can you take our bathroom spring scales to the Moon and
measure how much you weigh?
a. Yes. If you understand physics…
b. No. If you don’t understand the difference between mass
and weight.
Back
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × cm × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
What do you do to make the bathroom spring scale give correct
mass on the Moon?
a. Divide the reading by 6.
b. Multiply the reading by 6.
c. Divide the reading by 9.8
d. Multiple the reading by 9.8
Back
Question
Technically, the reading off the spring scales should be in unit of
force (such as Newton, or kg × cm × sec-2), not mass. However,
because we know how strong the gravitational acceleration is on
the surface of Earth, we had taken care to calibrate our scales
and we show our weight in mass unit (like kilo-gram or pound).
We also know that the gravitational acceleration on the surface of
the Moon is only about 1/6 of Earth’s.
Can you take a balance scale to the Moon and measure how
much you weigh?
a. Yes.
b. No.
As long as you have the standard
weights (mass really) with you!
 Back