Formula Sheet
Measurement & Vectors
• Distance: total path length (no direction)
• Displacement: change in position (has direction)
Δ𝑥 = 𝑥! − 𝑥"
• Average Speed:
Speed =
• Average Velocity:
Distance
.
Time
𝑣avg =
Δ𝑥
Δ𝑡
𝑎 =
Δ𝑣
Δ𝑡
• Acceleration:
• Dot Product:
I⃗ = |𝐴||𝐵| cos 𝜃
𝐴⃗ʘ𝐵
I⃗ = 𝐴& 𝐵& + 𝐴' 𝐵'
𝐴⃗ʘ𝐵
Motion in One Dimension (Constant Acceleration)
𝑣! = 𝑣" + 𝑎 𝑡
∆𝑑 = 𝑣" 𝑡 + (1/2)𝑎𝑡 (
𝑣!( = 𝑣"( + 2𝑎∆𝑑
∆𝑑 =
1
R𝑣 + 𝑣" S 𝑡
2 !
• Free fall (near Earth): a = 𝑔 = 9.8𝑚/𝑠 (
•
Density:
(downward)
!
ρ = "
where ρ is density, m is mass, and V is volume.
Newton’s Laws
•
At equilibrium: ∑ IF⃗ = 0
• In Motion:
∑ IF⃗ = ma
I⃗
1
Forces: Weight, Normal Force, and Friction
•
Weight:
•
Normal Force (horizontal surface):
•
Friction (opposes motion):
𝑊 = 𝑚𝑔
𝑁 = 𝑚𝑔
𝑓𝑠 = 𝜇) 𝑁
(static friction)
𝑓𝑘 = 𝜇* 𝑁
(kinetic friction)
Circular Motion
•
Centripetal Acceleration:
𝑎+ = 𝑣 ( /𝑟
•
Centripetal Force:
𝐹+ = 𝑚𝑣 ( /𝑟
•
Motion in a Horizontal Circle (Rope/String):
𝑇 = 𝑚𝑣 ( /𝑟
•
Car Turning on a Horizontal Flat Curve:
𝑣,-& = t𝜇) 𝑔𝑟
•
Banked Curve (no friction):
𝑡𝑎𝑛(𝜃) = 𝑣 ( /(𝑟𝑔)
2