Rotational Motion Flashcards
Derivation of v=u+at
a=dv/dt a dt = dv define limits and integrate both sides at = v (where limit is t and 0 on left, and v and u on right) at-0 = v - u rearrange to be v=u+at
Derivation of s=ut+1/2 (at^2)
ds/dt = u+at ds = (u+at) dt define limits and integrate both sides s = ut + 1/2 (at^2) where limits are s and 0 on the left, and t and 0 on the right s = ut + 1/2 (at^2)
Derivation of v^2 = u^2 + 2as
v = u + at square both sides v^2 = u^2 + 2uat + (a^2)(t^2) take common factor v^2 = u^2 + 2a(ut+1/2 (at^2)) substitute s=ut+1/2 (at^2) v^2 = u^2 + 2as
How do you find acceleration, velocity or displacement through differentiating?
a=dv/dt
v=ds/dt
remember the number of variables decreases as you go from displacement to velocity to acceleration, so you know whether to integrate or differentiate to get your answer
What are equations that link linear and angular motion?
s=rθ
v=rω
a=rα
What is the formula for angular velocity?
ω=2pi/T
or 2pi x no of revolutions/t
What are the formulas for central force?
F=mv^2/r
F=mrω^2
Note that tension/central force travels into a circle
What is torque and its formula?
the turning effect a force can produce
T=Fr
or T=Frsinθ if the force is applied at an angle
What is inertia and its formula?
an objects resistance to angular acceleration
I=mr^2
What is the formula linking torque and inertia?
T=Iα
What are the formulas for angular momentum?
L=Iω
L=mr^2ω
L=mvr
the right hand rule can be used for angular momentum. the thumb is the direction of angular momentum and the fingers are curled in the direction of rotation.
What is the formula for the total kinetic energy of a system that is moving linearly and rotationally?
Ek=1/2(Iω^2) + 1/2 (mv^2)
What is the formula for the force of gravity between two objects?
F=GMm/r^2
What is the formula for the gravitational force on a small object on earths surface?
w=mg F=GMm/r^2
mg=GMm/r^2
g=GM/r^2
What is a gravitational field?
the force per unit mass at that point
What is gravitational potential and its formula?
the work done in moving a unit mass from infinity to that point. Measured in V or Jkg^-1
v= -GM/r
What is the formula for potential energy in a gravitational field?
E=Vm
What is the formula for a satellites velocity?
v=(GMe/r)^0.5
What is escape velocity and its formula?
the minimum velocity neeed for a mass to escape a gravitational field
v=(2GM/r)^0.5
this can be derived by:
Ek+Ep=0
substitute kinetic energy formula and Vm and rearrange
What is the formula for a satellite changing orbits?
E=GMeM/2r
What is general relativity?
the ideas behind a non inertial (accelerating) frame of reference eg equivalence principle or time dilation
What is a black hole?
a dense star with an escape velocity greater than the speed of light
What is the formula for the schwarzchild radius and its derivation?
escape velocity: v=(2GM/r)^0.5 since the escape velocity > c c=(2GM/r)^0.5 c^2=2GM/r r=2GM/c^2
What is the formula for power of a star?
P=kAT^4
