Circular Motion and Gravity Flashcards
Velocity of object moving in a circle with constant speed?
Changing velocity (due to direction change)
–> centripetal acceleration
Cause of acceleration
Unbalanced force acting in same direction
|
(Causing centripetal acceleration)
Centripetal force
Requirements to be a centripetal force
Direction of force must be at right angles to the direction of motion
Consequences of a centripetal force on motion of object
Object will have circular motion
Direction of F and acceleration will be towards the center of the circular path
E.g.s of Centripetal forces
String tied to ball swung in a circle
Fiction between a car’s tyres and the road
Centripetal acceleration
Object moving in circle of radius r and speed s
v2
a.(centripetal) = ———-
r
Size of force causing centripetal acceleration
F(c) = m a(c)
Formula for F(c)
m v2
F(c) = ——–
r
velocity v of an object moving in a circle
s
v = ——-
t
most easily found by dividing the circumference of the circle by the time for 1 revolution
2 pie r v = -----------
T
w = 2 pie / T. ( w = rv )
Newton’s Law of Universal Gravitation
Any two objects are attracted by a gravitational force
( any object with a mass exerts a gravitational pull)
Size of force depends on:
- The mass M & m of both objects
F ~ Mm
- The distance r between the two objects
F ~ 1 / r2
Combining these 2 gives
Mm F ~ ---------
r2
Formula for gravitational force F(g) between two objects
GMm
F = ———
r2
G is the Universal Gravitational Constant = 6.67 x 10^-11 N m^2 kg^-1
Gravitational Field Strength
Force (g)
Measured using the size of the F on a 1kg mass
F(g) = mg
Equation for gravitational field strength
g = GM / r^2
Why does a(g) = g?
F(g) = ma
F(g) = mg
a = g
What is the force F acting on a satellite in circular orbit?
GMm
1. Force of gravity on satellite F(g) = ———–
r^2
- Centripetal force keeping satellite in orbit
mv^2
F(c) = ————-
r
These 2 terms are = F(c) = F(g)
==> v^2 / r = GM / r^2
a(c) = g
