AP Physics 1: Unit 6 Circular Motion Formulas

Study Notes

Circular Motion Concepts

Centripetal Acceleration: Calculated using ( a_c = \frac{v^2}{R} ), it measures the acceleration of an object moving in a circle, directed towards the center. Units are m/s².
Centripetal Force: Given by ( F_c = m a_c ) or ( F_c = \frac{m v^2}{R} ), it is the net force causing centripetal acceleration, measured in Newtons (N).

Waves and Frequencies

Period: The time taken to complete one full cycle of motion is calculated using ( T = \frac{1}{f} ), where T is in seconds.
Frequency: The number of cycles per second, expressed as ( f = \frac{1}{T} ), with the unit Hertz (Hz), equivalent to 1/s.

Circular Motion Quantities

Circular Velocity: Determined by the formula ( v = \frac{\text{circumference}}{\text{time}} = \frac{2\pi R}{T} ) or ( v = 2\pi R f ), representing the linear speed of an object in circular motion.

Gravitation Laws

Newton's Law of Universal Gravitation: States that the gravitational force ( F_g = \frac{GMm}{R^2} ) depends on the product of the masses (M and m) and inversely on the square of the distance (R) between their centers. Key variables include:
- M: mass of the planet
- m: mass of the object
- R: distance between the centers
- G: gravitational constant

Gravitational Concepts

Gravitational Field Strength: Defined as ( g = \frac{GM}{R^2} ) where g is the acceleration due to gravity expressed in m/s². Derived from the universal gravitation formula. R can be the distance to the center of the mass.
Orbital Speed: Given by ( v = \sqrt{\frac{GM}{R}} ), it shows the relationship between gravitational force and centripetal force. Increases with M and decreases with R.

Orbital Dynamics

Orbital Period: Represented by ( T = \sqrt{\frac{4\pi^2 R^3}{GM}} ). It describes the time taken for one complete orbit. An increase in R leads to a longer period, while an increase in M results in a shorter period.

Description

Test your knowledge of key formulas related to circular motion and gravitation with this flashcard quiz. Each card presents a fundamental formula, including those for centripetal acceleration, centripetal force, period, and frequency. Perfect for AP Physics 1 students preparing for exams!