AP Physics 1: Unit 6 Circular Motion Formulas

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Questions and Answers

What is the formula for Centripetal Acceleration?

  • ac = R / v^2
  • ac = v^2 / R (correct)
  • ac = v / R
  • ac = mv^2

What is the formula for Centripetal Force?

  • Fc = mac (correct)
  • Fc = Fg
  • Fc = mv^2 / R (correct)
  • Fc = mgh

What is the Period (T) formula?

T = 1/f

What is the Frequency (f) formula?

<p>f = 1 / T</p> Signup and view all the answers

What is the formula for Circular Velocity?

<p>v = 2Ï€R / T</p> Signup and view all the answers

What is Newton's Law of Universal Gravitation formula?

<p>Fg = GMm / R^2</p> Signup and view all the answers

What is the Gravitational Field Strength formula?

<p>g = GM / R^2</p> Signup and view all the answers

What is the formula for Orbital Speed?

<p>v = √(GM / R)</p> Signup and view all the answers

What is the formula for Orbital Period?

<p>T = √(4π^2R^3 / GM)</p> Signup and view all the answers

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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.

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