College 1: chapter 2, 3, 4
1
𝑥(𝑡) = 𝑎𝑡 2 + 𝑣0 𝑡 + 𝑥0
2
𝑑
→ 𝑣(𝑡) = 𝑥(𝑡) = 𝑎𝑡 + 𝑣0
𝑑𝑡
𝑑 𝑑2
→ 𝑎(𝑡) = 𝑎 = 𝑣(𝑡) = 2 𝑥(𝑡) = independent of time (a = constant)
𝑑𝑥 𝑑𝑥
free fall acceleration: 𝑎 = −𝑔 = −9.8 𝑚/𝑠 2
𝑎 = 𝑎𝑥 𝑖̂ + 𝑎𝑦 𝑗̂ with |𝑎| = √𝑎2 𝑥 + 𝑎2 𝑦
the unit vectors have a magnitude of 1
if we only have the magnitude and angle given: use sin or cos to define 𝑎𝑥 and/or 𝑎𝑦
velocity has a direction, speed doesn’t care about direction
𝛥𝑟 = 𝑟2 − 𝑟1 = (𝑥2 − 𝑥1 )𝑖̂ + (𝑦2 − 𝑦1 )𝑗̂ + (𝑧2 − 𝑧1 )𝑘̂
k is only if we have a 3rd dimension
𝛥𝑟 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑣𝑎𝑣𝑔 = 𝛥𝑡
but 𝑠𝑎𝑣𝑔 = 𝛥𝑡
𝑔
parabolic motion (2D): 𝑦(𝑥) = (𝑡𝑎𝑛 𝛼0 )𝑥 − 2(𝑣 𝑐𝑜𝑠 𝛼0 )2
𝑥2
𝑜
𝑣20
horizontal range: 𝑅 = 𝑠𝑖𝑛 2𝜃0
𝑔
1
vertical distance (like jumping from somewhere oid) 𝑦 = 𝑦0 − 2 𝑔𝑡 2
𝑦
𝜃 = 𝑡𝑎𝑛−1 ( )
𝑥
Quiz answers:
when you toss a ball straight up, the vertical component of its velocity at its highest point is zero
,Summary Principle of Physics
, College 2: chapter 5, 6
Newton’s 1st law (law of inertia):
if the net force acting on a body =0 (𝐹𝑛𝑒𝑡 = 0), then the velocity of the body remains constant (no acceleration)
Newton’s 2nd law:
𝐹𝑛𝑒𝑡 = 𝑚 ⋅ 𝑎 = ∑ 𝐹𝑖
𝑖
→ 𝐹3 = 𝑚 ⋅ 𝑎 − 𝐹2 − 𝐹1
𝐹3,𝑥 = 𝑚𝑎𝑥 − 𝐹2,𝑥 − 𝐹1,𝑥 = 𝑚(𝑎 𝑐𝑜𝑠50) − 𝐹2 𝑐𝑜𝑠(90) − 𝐹1 𝑐𝑜𝑠(210)
1
𝑥(𝑡) = 𝑎𝑡 2 + 𝑣0 𝑡 + 𝑥0
2
𝑑
→ 𝑣(𝑡) = 𝑥(𝑡) = 𝑎𝑡 + 𝑣0
𝑑𝑡
𝑑 𝑑2
→ 𝑎(𝑡) = 𝑎 = 𝑣(𝑡) = 2 𝑥(𝑡) = independent of time (a = constant)
𝑑𝑥 𝑑𝑥
free fall acceleration: 𝑎 = −𝑔 = −9.8 𝑚/𝑠 2
𝑎 = 𝑎𝑥 𝑖̂ + 𝑎𝑦 𝑗̂ with |𝑎| = √𝑎2 𝑥 + 𝑎2 𝑦
the unit vectors have a magnitude of 1
if we only have the magnitude and angle given: use sin or cos to define 𝑎𝑥 and/or 𝑎𝑦
velocity has a direction, speed doesn’t care about direction
𝛥𝑟 = 𝑟2 − 𝑟1 = (𝑥2 − 𝑥1 )𝑖̂ + (𝑦2 − 𝑦1 )𝑗̂ + (𝑧2 − 𝑧1 )𝑘̂
k is only if we have a 3rd dimension
𝛥𝑟 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑣𝑎𝑣𝑔 = 𝛥𝑡
but 𝑠𝑎𝑣𝑔 = 𝛥𝑡
𝑔
parabolic motion (2D): 𝑦(𝑥) = (𝑡𝑎𝑛 𝛼0 )𝑥 − 2(𝑣 𝑐𝑜𝑠 𝛼0 )2
𝑥2
𝑜
𝑣20
horizontal range: 𝑅 = 𝑠𝑖𝑛 2𝜃0
𝑔
1
vertical distance (like jumping from somewhere oid) 𝑦 = 𝑦0 − 2 𝑔𝑡 2
𝑦
𝜃 = 𝑡𝑎𝑛−1 ( )
𝑥
Quiz answers:
when you toss a ball straight up, the vertical component of its velocity at its highest point is zero
,Summary Principle of Physics
, College 2: chapter 5, 6
Newton’s 1st law (law of inertia):
if the net force acting on a body =0 (𝐹𝑛𝑒𝑡 = 0), then the velocity of the body remains constant (no acceleration)
Newton’s 2nd law:
𝐹𝑛𝑒𝑡 = 𝑚 ⋅ 𝑎 = ∑ 𝐹𝑖
𝑖
→ 𝐹3 = 𝑚 ⋅ 𝑎 − 𝐹2 − 𝐹1
𝐹3,𝑥 = 𝑚𝑎𝑥 − 𝐹2,𝑥 − 𝐹1,𝑥 = 𝑚(𝑎 𝑐𝑜𝑠50) − 𝐹2 𝑐𝑜𝑠(90) − 𝐹1 𝑐𝑜𝑠(210)
