centripetal force and gravity Flashcards
abbreviations
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centripetal force
a body is kept moving in a circle by a force called the centripetal force, acting towards the centre of the circle
F = mv²/r (incl notation)
the force required depends on:
- the mass of the body
- the speed of the body
- inversely on the radius of the circle
uniform circular motion
if a body is in uniform circular motion, its velocity is constant in magnitude but not in direction, so it has acceleration
periodic time (T)
the time for one complete revolution
Radians
angles can also be measured in radians
If the circumference length is equal to the raidus, the angle is 1 radians
angle in radians formula
arc length / radius
radians and degrees
180° = π radians
= 3.14159 rad
equations
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centripetal acceleration
if a body is moving in a circle the acceleration it has towards the centre of the circle is called the centripetal acceleration
gravity (Acceleration due to)
- Ignoring air resistance, the acceleration due to gravity is the same for all bodies at the same place
- A body falling freely experiences an acceleration g towards the centre of the earth
- It is always downwards
- 9.8 m/s⁻²
Kepler
in 1609 Kepler published his laws of planetary motion which discussed gravity. He published 3 laws
Kepler laws
1- The planets move in elliptical orbits round the sun as one focus
2- the line joining the sun and the planets sweeps out equal areas in equal time intervals
3- the square of the periodic time of a planet is proportional to the cube of its distance from the sun
Kepler’s Third Law
for the planets + the Moon, the square of the period of the orbit is directly proportional to the cue of the radius of the orbit
Kepler equations
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Derivations
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circular satellite orbits
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centripetal force
centripetal force = force of gravity
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