Chapter 1
Chapter 1
Density
Significant Figures: Multiplication
Mechanics
Chapter 1
Mechanics
Chapter 2
Significant Figures: Addition
Displacement
Mechanics
Chapter 2
Mechanics
Chapter 2
Average velocity
Average speed
Mechanics
Chapter 2
Mechanics
Chapter 2
Instantaneous velocity
Average acceleration
Mechanics
Chapter 2
Mechanics
Chapter 2
Instantaneous acceleration
Mechanics
Velocity as a function of time
Mechanics
When multiplying several quantities, the
number of significant figures in the final
answer is the same as the number of significant figures in the quantity having the
lowest number of significant figures. The
same rule applies to division.
∆x ≡ xf − xi
or
Displacement = area under the vx –t graph
Average speed =
āx ≡
total distance
total time
∆vx
vxf − vxi
=
∆t
tf − ti
ρ≡
When numbers are added or subtracted,
the number of decimal places in the result
should equal the smallest number of decimal places of any term in the sum.
v̄x ≡
vx ≡ lim
∆t→0
vxf = vxi + ax t
(constant acceleration)
m
V
ax ≡ lim
∆t→0
∆x
∆t
∆x
dx
=
∆t
dt
∆vx
dvx
=
∆t
dt
Chapter 2
Chapter 2
Position as a function of velocity and time
Position as a function of time
Mechanics
Chapter 2
Mechanics
Chapter 3
Velocity as a function of position
Polar =⇒ Cartesian
Mechanics
Chapter 3
Mechanics
Chapter 3
Cartesian =⇒ Polar
Scalar quantity
Mechanics
Chapter 3
Mechanics
Chapter 4
Vector quantity
Velocity vector as a function of time
Mechanics
Chapter 4
Mechanics
Chapter 4
Position vector as a function of time
Mechanics
Centripetal acceleration
Mechanics
1
xf = xi + vxi t + ax t
2
(constant acceleration)
xf = xi +
1
(vxi + vxf ) t
2
(constant acceleration)
2
2
vxf
= vxi
+ 2ax (xf − xi )
x = r cos θ
y
= r sin θ
A value with magnitude only and no associated direction
(constant acceleration)
r
tan θ
vf = vi + at
ac =
v2
r
=
p
=
y
x
x2 + y 2
A value that has both magnitude and direction
1
rf = ri + vi t + at2
2
Chapter 4
Chapter 4
Period of circular motion
Total acceleration
Mechanics
Chapter 4
Mechanics
Chapter 5
Galilean Transformation
Newton’s First Law
Mechanics
Chapter 5
Mechanics
Chapter 5
Newton’s Second Law
Newton’s Third Law
Mechanics
Chapter 6
Mechanics
Chapter 6
Force causing centripetal acceleration
Nonuniform circular motion
Mechanics
Chapter 7
Mechanics
Chapter 7
Scalar, dot or inner product
Mechanics
Work done by a constant force
Mechanics
a = at + ar =
d|v|
v2
θ̂ − r̂
dt
r
T ≡
In the absence of external forces, when
viewed from an inertial reference frame, an
object at rest remains at rest and an object in motion continues in motion with a
constant velocity (that is, with a constant
speed in a a straight line).
When no force acts on an object, the
2πr
v
r0
= r − v0 t
v0
= v − v0
acceleration of the object is zero
If two objects interact, the force F12 exerted by object 1 on object 2 is equal in
magnitude and opposite in direction to the
force F21 exerted by object 2 on object 1:
When viewed from an inertial reference
frame, the acceleration of an object is directly proportional to the net force acting
on it and inversely proportional to its mass.
X
F12 = −F21
X
F=
X
Fr +
X
W ≡ F ∆r cos θ
Ft
X
A·B
A·B
F = ma
F = mac = m
v2
r
= AB cos θ
= Ax Bx + Ay By + Az Bz
Chapter 7
Chapter 7
Work done by a varying force
Mechanics
Spring force
Mechanics
Fs = −kx
Z
xf
W =
Fx dx
xi