List of Equations
opposite side
sin 𝜃 =
hypotenuse
cos 𝜃 =
adjacent side
hypotenuse
tan 𝜃 =
opposite side
adjacent side
𝑥2 = 𝑥1 + 𝑣𝑥,1 𝑡
1
𝑦2 = 𝑦1 + 𝑣𝑦,1 𝑡 − 𝑔𝑡 2
2
𝑣𝑥,2 = 𝑣𝑥,1
𝑣𝑦,2 = 𝑣𝑦,1 − 𝑔𝑡
𝑣𝑥,1 = 𝑣1 cos 𝛼
d 𝑛
𝑥 = 𝑛𝑥 𝑛−1
d𝑥
𝑣𝑦,1 = 𝑣1 sin 𝛼
𝑇=
2𝑣1 sin 𝛼
𝑔
𝑅=
𝑣12 sin 2𝛼
𝑔
⃗𝑨 = 𝐴𝑥 𝒊̂ + 𝐴𝑦 𝒋̂
𝐴 = √𝐴2𝑥 + 𝐴2𝑦
𝐴𝑦
𝜃 = tan−1 ( )
𝐴𝑥
ℎ𝑚𝑎𝑥 =
𝑣12 sin2 𝛼
𝑔
∑ ⃗𝑭 = 0
𝑣𝑎𝑣−𝑥 =
Δ𝑥
Δ𝑡
Δ𝑥 d𝑥
=
Δ𝑡→0 Δ𝑡
d𝑡
𝑣𝑥 = lim
𝑎𝑎𝑣−𝑥 =
⃗
∑ ⃗𝑭 = 𝑚𝒂
⃗𝑭A on B = −𝑭
⃗ B on A
Δ𝑣𝑥
Δ𝑡
𝑤 = 𝑚𝑔
𝑓𝑘 = 𝜇𝑘 𝑛
Δ𝑣𝑥 d𝑣𝑥
𝑎𝑥 = lim
=
Δ𝑡→0 Δ𝑡
d𝑡
𝑣𝑥,2 = 𝑣𝑥,1 + 𝑎𝑥 𝑡
1
𝑥2 − 𝑥1 = 𝑡(𝑣𝑥,1 + 𝑣𝑥,2 )
2
1
𝑥2 = 𝑥1 + 𝑣𝑥,1 𝑡 + 𝑎𝑥 𝑡 2
2
𝑓𝑠 ≤ 𝜇𝑠 𝑛
𝑎𝑟𝑎𝑑 =
𝑣 2 4𝜋 2 𝑅
=
= 𝜔2 𝑅
𝑅
𝑇2
𝑣=
2𝜋𝑅
𝑇
𝜔=
2
2
𝑣𝑥,2
= 𝑣𝑥,1
+ 2𝑎𝑥 (𝑥2 − 𝑥1 )
2𝜋
𝑇
𝑊 = 𝐹𝑠 cos 𝜙
⃗ = 𝑥𝒊̂ + 𝑦𝒋̂
𝒓
Δ𝑥
Δ𝑦
𝒊̂ +
𝒋̂
Δ𝑡
Δ𝑡
𝐹𝑠 = −𝑘𝑥
d𝑥
d𝑦
𝒊̂ +
𝒋̂
d𝑡
d𝑡
1
1
𝑊𝑏𝑦 𝑠𝑝𝑟𝑖𝑛𝑔 = 𝑘𝑥12 − 𝑘𝑥22 = −𝑊𝑜𝑛 𝑠𝑝𝑟𝑖𝑛𝑔
2
2
⃗ 𝑎𝑣 =
𝒗
⃗ =
𝒗
1
1
𝑊𝑛𝑒𝑡 = 𝑚𝑣22 − 𝑚𝑣12
2
2
Δ𝑣𝑦
Δ𝑣𝑥
⃗ 𝑎𝑣 =
𝒂
𝒊̂ +
𝒋̂
Δ𝑡
Δ𝑡
𝑃𝑎𝑣 =
d𝑣𝑦
d𝑣𝑥
𝒊̂ +
𝒋̂
d𝑡
d𝑡
𝑃=
⃗ =
𝒂
Δ𝑊
Δ𝑡
d𝑊
d𝑡
𝑈𝑔𝑟𝑎𝑣 = 𝑚𝑔𝑦
Useful Constants:
𝑔 = 9.80 m/s2
1
𝑈𝑒𝑙 = 𝑘𝑥 2
2
𝐾1 + 𝑈𝑡𝑜𝑡𝑎𝑙,1 + 𝑊𝑛𝑐 = 𝐾2 + 𝑈𝑡𝑜𝑡,2
𝑈𝑡𝑜𝑡𝑎𝑙 = 𝑈𝑔𝑟𝑎𝑣 + 𝑈𝑒𝑙
𝑊𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = −𝑓𝑠