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PHY2048 Exam 1 Formula Sheet
Vectors
~a =axˆ
i+ayˆ
j+azˆ
k~
b=bxˆ
i+byˆ
j+bzˆ
kMagnitudes: |~a|=qa2
x+a2
y+a2
z|~
b|=qb2
x+b2
y+b2
z
Scalar Product: ~a ·~
b=axbx+ayby+azbzMagnitude: ~a ·~
b=|~a||~
b|cos θ(θ= angle between ~a and ~
b)
Vector Product: ~a ×~
b= (aybz−azby)ˆ
i+ (azbx−axbz)ˆ
j+ (axby−aybx)ˆ
k
Magnitude: |~a ×~
b|=|~a||~
b|sin θ(θ= angle between ~a and ~
b)
Motion
Displacement: ∆~r =~r(t2)−~r(t1)
Average Velocity: ~vav e =∆~r
∆t=~r(t2)−~r(t1)
t2−t1
Average Speed: save = (total distance)/∆t
Instantaneous Velocity: ~v =d~r(t)
dt
Relative Velocity: ~vAC =~vAB +~vBC
Average Acceleration: ~aave =∆~v
∆t=~v (t2)−~v(t1)
t2−t1
Instantaneous Acceleration: ~a =d~v
dt =d2~r
dt2
Equations of Motion for Constant Acceleration
~v =~v0+~at
~r −~r0=~v0t+1
2~at2
v2
x=v2
x0+ 2ax(x−x0) (in each of 3 dim)
Newton’s Laws
~
Fnet = 0 ⇔~v is a constant (Newton’s First Law)
~
Fnet =m~a (Newton’s Second Law)
“Action = Reaction” (Newton’s Third Law)
Force due to Gravity
Weight (near the surface of the Earth) = mg ( use g=9.8 m/s2)
Magnitude of the Frictional Force
Static: fs≤µsFNKinetic: fk=µkFN
Uniform Circular Motion (Radius R, Tangential Speed v=Rω, Angular Velocity ω)
Centripetal Acceleration: a=v2
R=Rω2
Period: T=2πR
v=2π
ω
Projectile Motion
Range: R=v2
0sin(2θ0)
g
Quadratic Formula
If: ax2+bx +c= 0 Then: x=−b±√b2−4ac
2a
