Rotation, Gravity, and the Big Picture

Manual: General · Subject: Newtonian Mechanics

Close the course by connecting circular motion, universal gravitation, and the major ideas of Newtonian mechanics.

Beyond Straight-Line Motion

Circular motion

An object moving in a circle at constant speed is still accelerating because its velocity direction changes. The inward acceleration is called centripetal acceleration and has magnitude $a_c = \frac{v^2}{r}$ .

Centripetal force

The inward net force needed for circular motion is $F_c = m\frac{v^2}{r}$ . This force is not a new kind of force; it is the net inward force supplied by gravity, tension, friction, or another interaction.

Universal gravitation

Newton’s law of gravitation says that two masses attract each other with force $F = G\frac{m_1m_2}{r^2}$ , where $G$ is the gravitational constant and $r$ is the distance between their centers.

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One big idea

Newtonian mechanics explains many phenomena with a small number of laws: forces produce acceleration, momentum can be conserved, and energy methods often simplify the math.

Three major problem-solving tools

Newton’s laws

Best for finding forces and accelerations
Works in many situations
Requires a clear free-body diagram

Momentum

Best for collisions and explosions
Useful when external forces are small
Focuses on system behavior

What causes centripetal acceleration?

A force pointing outward from the center A change in speed only A change in the direction of velocity No force at all

Write the formula for gravitational force between two masses.

What to remember from the whole course

1

Step 1: Use coordinates and units carefully.
2

Step 2: Describe motion with velocity and acceleration.
3

Step 3: Draw forces using free-body diagrams.
4

Step 4: Apply Newton’s laws, momentum, and energy as appropriate.
5

Step 5: Choose the simplest method that fits the problem.

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