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PHYSICS
à
A vector quantity has both magnitude and direction
Ex: force, velocity,
acceleration, momentum
à
A scalar quantity has magnitude only
Ex: speed, energy,
temperature, electric charge
Resultant (Two Dimensions)
The resultant,
X ,
of forces
with components and
has
the magnitude of
The resultant direction
with respect to the -axis
using four-quadrant angle functions is
The vector form of the
force is
F = Fxi + Fyj
Resolution of a Force
à
à 
Separating a Force into Components
_______
where R = √x2 + y2
Friction
where
is the frictional force
 is
the coefficient of static friction
is the normal force between surfaces in contact.
Average Velocity
V = d/t
where d
total displacement
is the elapsed time.
Acceleration
a = V2 - V1
t2 - t1
where a is the instantaneous acceleration of the particle.
Straight Line Motion
d = V1t
+ ½ at2
V2 = V1
+ at
V22 = V12
+
2ad
Free-Falling Body
if downward
if upward
for free-fall motion, replace a with g = 9.8 m/s2 ;
use +g when the body is falling, -g when thrown upward
Projectile Motion
 
Concept of
Weight
where
is the weight in Newtons,
is the mass in kilograms, and
is the local acceleration of gravity in meters per second squared. Value
9.8 m/s
One-Dimensional Motion of Particle
When
referring to motion in the  -direction,
where
is the resultant of the applied forces in the
-direction.
If the force is
constant (independent of time, displace, or velocity),
Circular
Motion
Centripetal
acceleration,
ac=V2
r
where V
is the linear velocity and r is the radius
centripetal
acceleration is always directed towards the center of the circular path
Work and Energy
Work is defined as
Kinetic Energy
The kinetic energy of a
particle is the work done in moving the particle from rest to a
velocity,
In changing the
velocity from  to
 ,
the change in kinetic energy is
Potential
Energy
Gravitational
Potential Energy
where h is the elevation above a reference point
Elastic Potential
Energy
PE = ½ Kx2
where K is the spring constant & x is the elevation
or compression of the sprin
where
is the elevation above a specified datum.
Principle of Work and Energy
If
 and
 are
kinetic energy and potential energy at state i, then for
conservative systems (no energy dissipation), the law of conservation of
energy is
If non-conservative
forces are present, then the work done by these forces must be accounted
for
Impact
Momentum is conserved
while energy may or may not be conserved. For direct central impact with
no external forces
where
are the masses of the two bodies,
are the velocities before impact, and
are the velocities after impact. |
