Circular Motion & Gravitation Flashcards
An object moving along a circular path at constant speed is still accelerating. Why?
- Its direction of motion is constantly changing
- ∴ velocity is constantly changing
- acceleration is the rate of ∆ velocity
a = v^2/r = 4π^2r/T^2
- Only constant speed questions
a = acceleration (ms-2)
v = speed (ms-1)
r = radius of circle (m)
T = period (time for one revolution)(s)
F = mv^2/r
F = centripetal force (N)
m = mass (kg)
r = radius (m)
v = 2πr/T
v = speed (ms-1) (tangent to the circle)
r = radius of circle (m)
T = period (time for one revolution)(s)
ω = θ/t
ω = angular velocity (rads^-1)
θ = angular displacement (rad)
one revolution = 360° = 2π radians
T = 1/f
T = period (time for one revolution)(s)
f = frequency (Hz)
ω = 2π f
ω = angular velocity (rads^-1)
f = frequency (Hz)
not given
v = ωr
v = linear velocity (ms-1)
ω = angular velocity (rads^-1)
r = radius (m)
F = mω^2r
F = centripetal force (N)
m = mass (kg)
ω = angular velocity (rads^-1)
r = radius (m)
F = mv^2/r
F = centripetal force (N)
m = mass (kg)
v = linear velocity (ms-1)
r = radius (m)
Fc = mgtanθ
Fc = centripetal force (N)
m = mass (kg)
g = gravity (9.81 ms-2)
*ignore friction
v = √rgtanθ
- maximum speed for a banked corner of angle θ (if there is no sideways friction)
v = √rg
minimum speed needed to move in a vertical circle
- top of the circle (feel weightless) Fc = Fg
Fg = weight force
Ek (bottom) = Ek (top) + Ep (top)
Top of circle = some Ep + some Ek
Bottom = all Ek
Top of hill = all Ep
Newtons universal law of gravitation states:
“every single point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation”
*point mass = a mass which does not take up any space
F = G Mn/r^2
F = gravitational force (N)
M & m = mass (kg)
r = distance/radius (m)
G = gravitational constant = 6.67 x 10^-11 Nm^2kg^-2
Gravitational field is defined as :
“A region of space where a mass experences a force because of its mass”
Earth = radial
surface of earth = uniform
Gravitational field strength (g) is defined as:
“the force per unit mass experenced by a small point test mass placed in the field”
*A test mass is one that has such a small mass that it does not change the gravitational field in which it is placed
g = F/m
a = F/m
*assuming no air resistance
g = Gravitational field strength (Nkg^-1)
F = force (N)
m = mass (kg)
a = acceleration (ms^-2)
g = GM/r^2
*Gravitational field strength at a planet’s surface
r = radius (m) (from centre of planet)
g = Gravitational field strength (Nkg^-1)
G = gravitational constant = 6.67 x 10^-11 Nm^2kg^-2
M = mass (kg)
v (of satellite) = √GM/r
r = radius (m) (from centre of planet)
G = gravitational constant = 6.67 x 10^-11 Nm^2kg^-2
M = mass (kg)
v = speed of satellite (ms-1)
Centripetal force = Gravitational force
a (acceleration of a satellite) = Fg(or Fc)/m
or
a (acceleration of a satellite) = v^2/r
m = mass of satellite
Fg = gravitational force
Fc = centripetal force
v = speed of satellite
r = radius (m) (from centre of planet)
r^3 = GMT^2/4π^2
G, M, 4, π are all constants so r^3 ∝ T^2
i.e. r^3 / T^2 = constant (for anything orbiting a body of mass)
Angular displacement (θ)
angle (in radians) through which an object undergoing
circular motion has moved
angular velocity
(ω)
angular displacement divided by time taken
(units: rad s-1)
centripetal force
an unbalanced force that causes circular motion
frequency
number of revolutions per sec
geostationary orbit
an orbit around the Earth that has a period of 24 hours
(so the satellite remains above the same point on the
Earth’s surface)
Kepler’s 3rd Law
the cube of the radius of a satellite is proportional to the square of its period
period
time for one revolution
point mass
a mass which does not take up any space (i.e. it is infinitely small)
test mass
a mass that is so small it does not change the gravitational field in which it is placed
