Chapter 3: Inertia and Newton's Law of Motion
Published 2 years ago
Published 2 years ago
- Galileo developed the idea of inertia.
- Newton used it as his 1st law of motion.
- Net force = The sum of all forces pulling in various directions.
- If the net force = 0, inertia is constant.
- A body that is not moving will remain motionless = constant velocity.
- A moving body’s motion will remain constant at the same speed and in the same direction = constant velocity.
Speed and Velocity
- Speed is a change of position in some amount of time, such as m/s or km/h.
- Velocity is a speed in a particular direction.
- NOTE: The units, m/s, are still the same, which can cause confusion.
- If the speed remains constant, but the direction changes, the velocity changes.
Orbital Motion and Gravity
- Newton understood that orbiting objects, such as the Moon and Earth, have constantly changing velocity because of the changing direction.
- Newton realized that a force causes this changing velocity.
- When an object accelerates, its velocity changes.
- Its speed may increase in some length of time.
- Its speed may decrease in some time = a deceleration or a negative acceleration.
- If an object’s direction of motion changes its velocity changes even though its speed may remain constant = acceleration.
- Units are
- Mass - amount of matter in a body.
- Impossible to count the number of atoms and molecules in a body.
- Express the mass in kilograms (kg).
- Mass is NOT the same as weight.
- Weight is the force of gravity on a mass.
- Confusion is caused when people use the kg for both mass and weight - wrong.
- The unit of weight is the Newton.
Newton’s 2nd Law of Motion
- With the quantities we have defined, we can state Newton’s 2nd law of motion.
- A net force causes of body with a mass to accelerate and the relationship is acceleration = net force/mass (a=F/m)
- It is a simple equation, but it explains the motions of all objects on Earth, in the solar system, and throughout the Universe.
Newton’s 3rd Law of Motion
- When two objects interact with each other the force of object 1 on object 2 is equal to the force of object 2 on object 1.
- Action = Reaction
Newton’s Law of Gravitational Force
- Newton needed to develop a law for the force of gravity for his laws of motion.
- Force of gravity depends on all masses: for two objects these are M for the larger mass and m for the smaller mass.
- Force of gravity depends on the separation.
- Greater separation weaker force.
- Weakens as (1/separation) = “inverse square law”
- Force of gravity never goes to zero, no matter how far away.
- Newton’s equation:
- G = universal gravitational force constant.
- M = the mass (kg) of the larger object.
- m = the mass (kg) of the smaller object.
- d = the separation (m) between the two objects.
Gravity is important for Astronomy
- Astronomical objects have:
- Huge masses huge force of gravity.
- Huge separations weak force of gravity.
- Small separations huge force of gravity.
- Mass is only a positive quantity.
- Gravity cannot cancel out.
- Gravity never stops, even at the largest distances.
Earth and Moon
- The force of Earth’s gravity on the Moon is
- However, the Earth and Moon respond differently to the same force because they have different masses.
- For the Moon amoon = FG/mmoon
- For the Earth aEarth = FG/MEarth
- NOTE: The force of gravity causes both the Moon and Earth to accelerate.
- Measuring orbits is the fundamental way of measuring masses in astronomy.
- To make things simple, assume M>>m.
- Combine Newton’s 2nd law of motion and his law of gravity to get M = dV^2/G.
- The mass equation can be rewritten as a modified version of Kepler’s 3rd law
- Newton’s version:
- This can be used for any planet.
The Sun, Surface Gravity, Escape Velocity and Planets
The Mass of the Sun
- To measure the Sun’s mass we can use Earth’s orbit.
- d = 1 AU
- P = 1 year
- G =
- This results in about 300,000 MEarth
- We experience “surface gravity” here on Earth every day, and that would also be true on the Moon or another planet.
- Surface gravity is the acceleration caused by a planet’s (such as Earth) gravity.
- The surface gravity determines how fast an object must travel to escape into space.
- The equation can be found from Newton’s laws of motion and gravity.
- Earth’s escape velocity is found using its mass and radius.
- The moon’s escape velocity is much less because its mass and radius are less
Atmospheres of Planets
- A planet’s ability to have an atmosphere depends on two things:
- Distance from the Sun, which determines the temperature of the atmospheric gas: closer to the Sun the gas is hotter and moves faster (molecules in hot temperature are more active).
- The escape velocity of the planet.
- If the gas speed > escape speed, the planet cannot hold an atmosphere.