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⚿ Projectile Motion 抛运动Pāo yùndòng
- horizontal 横Héng: Δvx ≠ f(t) = 0; ax ≠ f(t) = 0 ;
- vertical 垂Chuí: Δay = 0 ; ay ≠ f(t)
⚿ Linear ↔ Relative Motion
- vJon,Jane: velocity of Jon with respect to Jane (wrt)
- vJon,Earth: velocity of Jon wrt Earth
⚿ Pure Circular Motion (vr=0)
PHET Simulation Ladybug rotation Trad Chinese English
Quantities
- s : arc length (distance along edge of circle)
- r : radius of circle
- θ = s / r (defn)
- full circle: s = 2 π r → θfull circle = s/r = 2 π
Key Relationships
| $$ \omega (t) = { { d \, \theta (t) } \over { d \, t} } $$ |
$$ \alpha (t) = { { d \, \omega (t) } \over { d \, t} } $$ |
| $$ \omega (t) = \int { \alpha (t) \, dt } $$ |
$$ \theta (t) = \int { \omega (t) \, dt } $$ |
Linear ↔ Rotational Quantities
| s(t) = r θ(t) | vt(t) = ω(t) r
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| ar = vt 2 / r | at = α r
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Special case of α(t) = 0
Today's Lecture: Knight Chapter 4 Powerpoints