Position as a function of time for an object with constant acceleration

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Position as a function of time for an object with
constant acceleration
Velocity as a function of time for an object with
constant acceleration
Derivative relationships between position,
velocity, and acceleration
Integral relationships between position,
velocity, and acceleration
Kinematic equations for projectile motion
time
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x(t) x0 v0xt ½axt2
vx(t) v0x axt
v(t) dx/dt a(t) dv/dt
x(t) x0 v0xt vx(t) v0x y(t) y0 v0yt -
½gt2 vy(t) v0y -gt
time
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time
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v0x v0cos(?) v0y v0sin(?)
v0x v0cos(?) v0y -v0sin(?)
v0x -v0cos(?) v0y -v0sin(?)
v0x v0sin(?) v0y -v0cos(?)
v0x -v0sin(?) v0y -v0cos(?)
Moving in negative (-) direction Accelerating in
positive () direction at 2 m/s2
Moving in positive () direction Accelerating in
negative (-) direction at -1 m/s2
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Statement of Newtons 1st Law
Statement of Newtons 2nd Law
Statement of Newtons 3rd Law
Integral relationship defining impulse
Magnitude and direction of the force of kinetic
friction
Magnitude and direction of the force of static
friction
Magnitude and direction of the force imparted by
a spring
Magnitude and direction of the force of gravity
on the surface of a planet
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F dp / dt ?p / ?t If mass is constant,
then F ma
An object does not change its state of motion
unless acted on by a net force. The state of
motion can be rest or linear motion at constant
speed.
All forces come in pairs. The two forces in a
pair act on different objects, are of the same
type, and are equal in magnitude but opposite in
direction.
?p F(t) dt If force is constant, then ?p F
?t
0 FS µSN Magnitude varies. Force acts to
oppose potential relative motion between two
surfaces.
FK µKN Force acts to oppose relative motion
between two surfaces.
Fg mg (g GM/R2) Force points to center of
planet.
FS -k(?x) Force acts to oppose stretching or
compressing of spring from equilibrium position
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Magnitude and direction of the force of gravity
between two objects
Newtons Gravitational Constant G
Speed of an object in circular motion
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Fg -Gm1m2 / r2 Forces acting on each object
point to the center of mass of the other object.
Fx Fcos(?) Fy Fsin(?)
Fx Fcos(?) Fy -Fsin(?)
Fx -Fcos(?) Fy -Fsin(?)
Fx Fsin(?) Fy -Fcos(?)
Fx -Fsin(?) Fy -Fcos(?)
v 2pR / T
G 6.6710-11 Nm2/kg2
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Net force on an object in circular motion
Determine the net force
Determine the net force
Determine the net force
Determine the net force
Determine the net force
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FNET
FNET mv2 / r
FNET
Zero net force
Zero net force
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Magnitude and direction of the force of air
resistance
Conversion from English pounds to Newtons
conversion from kilograms to pounds (on Earth)
Terminal velocity magnitude
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a gsin(?)
a gsin(?) -µKgcos(?)
a g (m2 m1) / (m1 m2)
a m1g / (m1 m2)
Fb bvn Force vector points opposite to the
velocity vector
Wx mgsin(?) Wy -mgcos(?)
If Fb bvn then vT (mg/b)1/n
1 lb 4.4 N 1 kg 2.2 lbs (on Earth)
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Derivative relationship between force and momentum
Definition of work (text)
Integral relationship defining impulse
Kinetic energy equation
Derivative relationship between force and
potential energy
Potential energy in a uniform gravitational field
Integral relationship defining work
Potential energy stored in a compressed or
stretched spring
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Work is the transfer of energy from one object or
system to another through the application of a
force.
F dp / dt ?p / ?t
?p F(t) dt If force is constant, then ?p F
?t
K ½ mv2 (or K p2/2m)
F -dU / dx -?U / ?x
U mgh
U ½ kx2
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Potential energy due to gravity a distance r from
a massive object
Kinetic energy of a rotating object
Integral relationship relating a conservative
force to potential energy
Rotational inertia of solid sphere rotated about
its center
M, R
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U -GMm/r
K ½ I?2
I ½MR2
I (1/3)ML2
I MR2
I (2/5)MR2
I (1/12)ML2
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Big Three equations for rotational motion
Definition of angular momentum
Derivative definitions of angular velocity and
angular acceleration
Relationship between angular velocity and
rotational period
Relationship between torque and angular momentum
Relationship between angular acceleration and
torque
Relationship between angular velocity and angular
momentum
Definition of torque
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L r p rpsin(?) r-p rp-
?(t) ?0 ?0t ½at2 ? ?0 at ?2 ?02
2a(??)
?(t) d? / dt a(t) d? / dt
? 2p / T
t dL/dt ?L/?t
a tNET / I
t r F rFsin(?) r-F rF-
L I?
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Differential equation describing simple harmonic
motion
Position and velocity of an object in simple
harmonic motion
Relationship between angular frequency and period
Relationship between frequency and period
Relationship between angular frequency and
frequency
Period of a simple pendulum in simple harmonic
motion
Period of a physical pendulum in simple harmonic
motion
Period of a mass on a spring in simple harmonic
motion
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x(t) A0sin(?t) v(t) ?A0cos(?t)
? 2p / T
f 1 / T
? 2pf
T 2p(l/g)½
T 2p(m/k)½
T 2p(I/mgL)½
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x(t) x0 v0t ½at2 Evaluate dx/dt
x(t) x0 v0t Evaluate dx/dt
h(x) f(x)g(x) Evaluate dh/dx
F bvn Evaluate dF/dv
h(x) f(g(x)) Evaluate dh/dx
x(t) Asin(t) Bcos(t) Evaluate dx/dt
Q(t) Q0e-t/t0 Evaluate dQ/dt
U(t) U0ln(r) Evaluate dU/dr
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x(t) x0 v0t dx/dt v0
x(t) x0 v0t ½at2 dx/dt v0 at
Product rule dh/dx f(x)(dg/dx) g(x)(df/dx)
F bvn dF/dv nbvn-1
Chain rule dh/dx (df/dg)(dg/dx)
x(t) Asin(t) Bcos(t) dx/dt Acos(t) -
Bsin(t)
U(t) U0ln(r) dU/dr U0 / r
Q(t) Q0e-t/t0 dQ/dt -(Q0/t0)e-t/t0
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TEMPLATE FOR CUTTING