Units to read: 14, 15, 16, 17,18

Mass and Inertia

• Mass is described by the amount of matter an object contains.

• This is different from weight – weight requires gravity or some other force to exist!

• Ex: while swimming, your weight may feel less because the body floats a little. Your mass, however, stays the same!

• Inertia is simply the tendency of mass to stay in motion

The Law of Inertia

• Newton’s First Law is sometimes called the Law of Inertia:

– A body continues in a state of rest, or in uniform motion in a straight line at a constant speed, unless made to change that state by forces acting on it

– Or, more simply, a body maintains the same velocity unless forces act on it

• A ball rolling along a flat, frictionless surface will keep going in the same direction at the same speed, unless something pushes or pulls on it

– Gravity!

Another View of Newton’s First Law

• If an object’s velocity is changing, there must be forces present!– Dropping a ball– Applying the brakes in a

car

• If an object’s velocity is not changing, either there are no forces acting on it, or the forces are balanced and cancel each other out– Hold a ball out in your

hand, and note that it is not moving

– Force of gravity (downward) is balanced by the force your hand applies (upward)!

Circular Motion

• Tie a string to a ball and swing it around your head

– Law of inertia says that the ball should go in a straight line

– Ball goes in a circle – there must be forces!

• Where’s the force?– It’s the tension in the string

that is changing the ball’s velocity

– If the string breaks, the ball will move off in a straight line (while falling to the ground)

Acceleration

• The term acceleration is used to describe the change in a body’s velocity over time– Stepping on the gas pedal of a

car accelerates the car – it increases the speed

– Stepping on the brakes decelerates a car – it decreases the speed

• A change in an object’s direction of motion is also acceleration– Turning the steering wheel of

a car makes the car go left or right – this is an acceleration!

– Forces must be present if acceleration is occurring

Newton’s Second Law

• The force (F) acting on an object equals the product of its acceleration (a) and its mass (m)

• F = m a

• We can rearrange this to be:• a = F/m

• For an object with a large mass, the acceleration will be small for a given force

• If the mass is small, the same force will result in a larger acceleration!

• Though simple, this expression can be used to calculate everything from how hard to hit the brakes to how much fuel is needed to go to the Moon!

Newton’s Third Law

• When two bodies interact, they create equal and opposite forces on each other

• If two skateboarders have the same mass, and one pushes on the other, they both move away from the center at the same speed

• If one skateboarder has more mass than the other, the same push will send the smaller person off at a higher speed, and the larger one off in the opposite direction at a smaller speed

– Why?

This works for planets, too!

Orbital Motion and Gravity

• Astronauts in orbit around the Earth are said to be in free fall, a weightless state.

– Are they falling? Yes!

• Imagine a cannon on top of a mountain that fires a cannonball parallel to the ground

• The cannonball leaves the cannon and is pulled toward the ground by gravity

• If the ball leaves the cannon with a slow velocity, it falls to the ground near the mountain

• If the cannonball has a higher velocity, if falls farther from the mountain.

• What if we gave the cannonball a very large velocity, so large that it “misses” the Earth?

• The cannonball would be in orbit around the Earth, and it would be falling!

Surface Gravity

• Objects on the Moon weigh less than objects on Earth

• This is because surface gravity is less– The Moon has less mass than the

Earth, so the gravitational force is less

• We let the letter g represent surface gravity, or the acceleration of a body due to gravity

• F = mg• On Earth, g = 9.8 m/s2

• g on the Moon is around 1/6 as much as on the Earth!

Consider a basketball player dribbling a ball. Which of the following statements

is *not* true

• a. The ball bounces because the court floor pushes up on it every time it hits;

• b. The floor experiences no acceleration due to the dribbling ball because its mass is so large compared to that of the ball.

• c. The ball exerts a force on the player's hand each time the two connect;

• d. The player's hand exerts an equal force each time the two connect.

Which of the following properties of an astronaut changes when she is standing on the Moon, relative

to when the astronaut is standing on Earth?

• a. Weight

• b. Mass

• c. Inertia

• d. All of the above

Centripetal Force

• If we tie a mass to a string and swing the mass around in a circle, some force is required to keep the mass from flying off in a straight line

• This is a centripetal force, a force directed towards the center of the system

• The tension in the string provides this force.

• Newton determined that this force can be described by the following equation:

d

VmFC

2×=

d

VmFC

2×=

• Orbital velocity:

Orbits

d

GMVcirc =

We can use this expression to determinethe orbital velocity (V) of a small mass orbiting a distance d from the center of a much larger mass (M)

Calculating Escape Velocity

• From Newton’s laws of motion and gravity, we can calculate the velocity necessary for an object to have in order to escape from a planet, called the escape velocity

R

GMVesc

2=

Newton’s Universal Law of Gravitation

• Every mass exerts a force of attraction on every other mass. The strength of the force is proportional to the product of the masses divided by the square of the distance between them– Simply put, everything pulls on

everything else

– Larger masses have a greater pull

– Objects close together pull more on each other than objects farther apart

• This is true everywhere, and for all objects– The Sun and the planets exert a

gravitational force on each other

– You exert a gravitational force on other people in the room!

What Escape Velocity Means

• If an object, say a rocket, is launched with a velocity less than the escape velocity, it will eventually return to Earth

• If the rocket achieves a speed higher than the escape velocity, it will leave the Earth, and will not return!

The Origin of Tides

• The Moon exerts a gravitational force on the Earth, stretching it! – Water responds to

this pull by flowing towards the source of the force, creating tidal bulges both beneath the Moon and on the opposite side of the Earth

High and Low Tides

As the Earth rotates beneath the Moon, the surface of the Earth experiences high and low tides

The Sun creates tides, too!

• The Sun is much more massive than the Moon, so one might think it would create far larger tides!

• The Sun is much farther away, so its tidal forces are smaller, but still noticeable!

• When the Sun and the Moon line up, higher tides, call “spring tides” are formed

• When the Sun and the Moon are at right angles to each other, their tidal forces work against each other, and smaller “neap tides” result.