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University Physics 1 - Formula Sheet One Dimensional Kinematics  ∆𝑥 ≡ 𝑥𝑓 – 𝑥𝑖 

Avg speed ≡

 𝑉𝑎𝑣𝑔 ≡

 

𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑒𝑑

∆𝑥

=

∆𝑡

𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒

𝑥𝑓 −𝑥𝑖 𝑡𝑓 −𝑡𝑖

𝑣 ≡ lim 𝑣𝑎𝑣𝑔 = lim ∆𝑡→0

𝑎𝑎𝑣𝑔 ≡

∆𝑣 ∆𝑡

=

𝑣𝑓 −𝑣𝑖

𝑡𝑓 −𝑡𝑖

 

∆𝑥

∆𝑡→0 ∆𝑡

Newton’s Laws of Motion  ∑ 𝐹 = 𝑚𝑎

 

𝑊 ≡ 𝐹𝑑 cos 𝜃 1 𝐾 ≡ 𝑚𝑣 2 2

𝑊𝑛𝑒𝑡 = ∆𝐾

1

𝑥 = 𝑥𝑜 + 𝑣𝑜 𝑡 + 2 𝑎𝑡 2 𝑣 2 = 𝑣02 + 2𝑎(𝑥 − 𝑥0 )

 𝑊 = 𝑚𝑔

|𝐹| = 𝑘𝑥

 𝑎𝑐 =

Work and Kinetic Energy 

∆𝑡→0 ∆𝑡

∆𝑡→0







𝑣2 𝑟

1

𝑊 = 𝑘𝑥 2 2

 𝑃=

𝑊 𝑡

= 𝐹𝑣

Potential Energy and Conservation of Energy   

𝑊𝑐 = −∆𝑈 𝑈𝑔𝑟𝑎𝑣 ≡ 𝑚𝑔𝑦 𝐸 ≡ 𝐾 +𝑈

∆𝑣

Constant linear acceleration 𝑣 = 𝑣𝑜 + 𝑎𝑡  1 𝑥 = 𝑥𝑜 + 2 (𝑣𝑜 + 𝑣)𝑡  

Applications of Newton’s Laws  𝑓𝑠 ≤ 𝜇𝑠 𝑁  𝑓𝑘 = 𝜇𝑘 𝑁

𝑎 ≡ lim 𝑎𝑎𝑣 = lim

 𝑈𝑠𝑝𝑟𝑖𝑛𝑔 ≡

 𝑊𝑛𝑐 = ∆𝐸

1

2

𝑘𝑥 2

Linear Momentum and Collisions 

𝑝 ≡ 𝑚𝑣

 ∑ 𝐹 = lim

∆𝑝

∆𝑡→0 ∆𝑡 ∆𝑝

 ∑ 𝐹𝑎𝑣𝑔 = ∆𝑡  𝐼= ∑ 𝐹𝑎𝑣𝑔 ∆𝑡  𝐼 = ∆𝑝

 𝑋𝑐𝑚 =

∑ 𝑚𝑖 𝑥𝑖

=

𝑚1 𝑥1 +𝑚2 𝑥2 +⋯

 𝑌𝑐𝑚 =

∑ 𝑚𝑖 𝑦𝑖

=

𝑚1 𝑣1 +𝑚2 𝑣+⋯

∑ 𝑚𝑖

∑ 𝑚𝑖

𝑚1 +𝑚2 +⋯

𝑚1 +𝑚2 +⋯

Rotational Kinematics and Energy  𝜃≡

𝑠

𝑟

 ∆𝜃 ≡ 𝜃𝑓 − 𝜃𝑖  𝜔𝑎𝑣𝑔 ≡

∆𝜃

∆𝑡 ∆𝜃

 𝜔 ≡ lim  𝛼𝑎𝑣𝑔

𝜃𝑓 −𝜃𝑖 𝑡𝑓 −𝑡𝑖

∆𝑡→0 ∆𝑡 ∆𝜔 𝜔𝑡 −𝜔𝑖 ∆𝑙

=

Δ𝜔 ∆𝑡→0 Δ𝑡 2𝜋

 𝛼 ≡ lim  𝑇=

=

𝜔

 𝑣𝑡 = 𝑟𝜔  𝑎𝑡 = 𝑟𝛼  𝑎𝑐𝑝 = 𝑟𝜔2

𝑙𝑡 −𝑙𝑖

.

 Constant angular acceleration  𝜔 = 𝜔𝑜 + 𝛼𝑡 1  𝜃 = 𝜃𝑜 + (𝜔𝑜 + 𝜔)𝑡 2



1

θ = 𝜃𝑜 + 𝜔𝑜 𝑙 + 2 𝛼𝑡 2



 𝜔2 = 𝜔02 + 2𝛼(𝜃 − 𝜃𝑎 ) 2 2 2 𝐼 ≡ ∑𝑁 𝑖=1 𝑚𝑖 𝑟𝑖 = 𝑚1 𝑟1 + 𝑚2 𝑟2 + ⋯ 𝑚𝑁 𝑟𝑁2 (N point masses) 1

 𝐾𝑟𝑜𝑡 ≡ 𝐼𝜔2 2

 𝐾𝑡𝑜𝑡𝑎𝑙 = 𝐾𝑡𝑟𝑎𝑛𝑠 + 𝐾𝑟𝑜𝑡 = 1

𝐼 𝜔 2 𝑐𝑚

2

1

2

2 𝑀𝑣𝑐𝑚 +

Moments of Inertia for Uniform, Rigid Objects of Various Shapes

Rotational Dynamics and Static Equilibrium    

𝜏 ≡ 𝑟𝐹 sin 𝜃 ∑ 𝜏 = 𝐼𝛼 𝐿 ≡ 𝐼𝜔 𝐿 = 𝑟𝑚𝑣 sin 𝜃

Gravity

 𝐹𝑔𝑟𝑎𝑣 = 𝐺

 ∑𝜏 =

∆𝑡

 𝑊 = 𝜏𝜃

𝑚1 𝑚2 𝑟2

𝐺 = 6.67 ∙ 10

 𝑈𝑔𝑟𝑎𝑣 = −𝐺

∆𝐿

−11

𝑚1 𝑚2 𝑟

𝑁 ∙ 𝑚2 𝑘𝑔2

 𝑇2 =

4𝜋2 3 𝑟 𝐺𝑀 2𝐺𝑀

 𝑣𝑡 = √

𝑅

A list of solar system data is located at the end of the formula sheet

Solar System Data       

Radius of Earth: RE=6.37x106 m Radius of Moon: RM=1.74x106 m Mass of Earth: ME=5.97x1024 kg Mass of Moon: 7.35x1022 kg Mass of Sun: 2.00x1030 kg Earth-Moon distance: 3.84x108 m Earth-Sun distance: 1.50x1011 m...