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Questions and Answers
What is the formula for Centripetal Acceleration?
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?
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?
What is the Period (T) formula?
T = 1/f
What is the Frequency (f) formula?
What is the Frequency (f) formula?
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What is the formula for Circular Velocity?
What is the formula for Circular Velocity?
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What is Newton's Law of Universal Gravitation formula?
What is Newton's Law of Universal Gravitation formula?
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What is the Gravitational Field Strength formula?
What is the Gravitational Field Strength formula?
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What is the formula for Orbital Speed?
What is the formula for Orbital Speed?
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What is the formula for Orbital Period?
What is the formula for Orbital Period?
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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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