Chapter 4Motion, Energy, and Gravity

• Description of Motion• Mass and Weight• Newton’s Law of Motion• Newton’s Law of Gravity• Conservation Laws

PrefaceSo 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 ConceptsThese 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− Conservation of momentum

Description of MotionWhen we talk about motion, we need to talk about• Position: the position of an object with respect to a reference

point.– We specify position in length units, such as [meter], [foot], [kilo-

meter], [light-year], etc.• Velocity: change in position with respect to a reference point in

a given amount of time.– 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.

– 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 MotionThe 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.

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• Or, in angular coordinate system.

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Y

Examples of Acceleration

• Acceleration is not just speeding up or slowing down. When you are changing direction, you have acceleration also!

• Acceleration: speeding up

• 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 non-

zero acceleration.

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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 MassIn 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…

• 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

• 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!

QuestionTechnically, 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

QuestionTechnically, 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

QuestionTechnically, 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 9.8d. Multiple the reading by 9.8

Answer

QuestionTechnically, 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

QuestionTechnically, 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 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

r

QuestionTechnically, 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 9.8d. Multiple the reading by 9.8

Back

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.

Back

Question

As long as you have the standard weights (mass really) with you!