Formula Sheet for Physics 1D03
It is the student’s responsibility to know whether the formulae are correct and when they can be used.
𝒗≡
𝑑𝒓
𝑑𝑡
𝒂≡
𝑑𝒗
𝑑𝑡
𝑀𝒗𝒄𝒎 = [ 𝑚0 𝒗𝒊 = 𝒑𝒕𝒐𝒕𝒂𝒍
0
1
𝒓(𝑡) = 𝒓𝟎 + 𝒗𝟎 𝑡 + 𝒂𝑡 "
2
𝑣# = 𝑣$# + 𝑎# 𝑡
1
𝑥 = 𝑥$ + 𝑣$# 𝑡 + 𝑎# 𝑡 "
2
𝑣#" − 𝑣$" = 2𝑎# (𝑥 − 𝑥$ )
𝑣⃗9, < + 𝑣⃗<, 3 = 𝑣⃗9, 3
∑𝑭𝒆𝒙𝒕 = 𝑚𝒂𝒄𝒎 =
𝑑𝒑
𝑑𝑡
𝑓+ = 𝜇+ 𝑁
𝑓* ≤ 𝜇* 𝑁
𝐹* = −𝑘𝑥
𝑎, =
𝑎- = 𝑟𝛼
𝑎, = 𝑟𝜔"
𝜔 = 𝜔$ + 𝛼𝑡
1
𝜃 − 𝜃$ = 𝜔$ 𝑡 + 𝛼𝑡 "
2
𝜔" − 𝜔$" = 2𝛼(𝜃 − 𝜃$ )
𝐼 = [ 𝑚0 𝑟0"
0
𝐼 = 𝐼38 + 𝑀𝐷"
𝜏 = 𝑟𝐹 sin 𝜙 = 𝐹𝑑
𝜏⃗ = 𝑟⃗ × 𝐹⃗
𝑣"
𝑟
𝐿 = 𝐼𝜔
𝐿 = 𝑚𝑣𝑟 sin 𝜙
𝑑|𝒗|
𝑎- =
𝑑𝑡
𝑊 = ∫ 𝐹# 𝑑𝑥 (motion along 𝑥 axis)
𝑊 = 𝑭 ⋅ 𝒅 (consta𝑛𝑡 force)
𝑑𝑊
𝑃=
=𝑭⋅𝒗
𝑑𝑡
𝐾=
𝑠 = 𝑟𝜃
𝑣 = 𝑟𝜔
1
𝑚𝑣 "
2
𝑈. = 𝑚𝑔𝑦
1
𝑈* = 𝑘𝑥 "
2
𝑳=𝒓×𝒑
𝑑𝐿
𝜏 = 𝐼𝛼 =
𝑑𝑡
1
𝐾 = 𝐼𝜔"
2
1
1
"
𝐾 = 𝐼38 𝜔" + 𝑚𝑣38
2
2
𝑊 = 𝜏Δ𝜃
𝑃 = 𝜏𝜔
𝐾/ + 𝑈/ = 𝐾0 + 𝑈0 + 𝑊1.3.
𝑥 = 𝐴 cos(𝜔𝑡 + 𝜙)
𝒑 = 𝑚𝒗
𝜔 = 2𝜋𝑓 =
-!
X 𝛥𝑡 = 𝛥𝒑
𝑰 ≡ W 𝑭𝑑𝑡 ≡ 𝑭
-"
𝑀𝒓𝒄𝒎 = [ 𝑚0 𝒓𝒊
0
𝑘
𝜔=l
𝑚
2𝜋
𝑇
𝜔=m
𝑔
ℓ
𝑚𝑔𝑑
𝜔=l
𝐼