Physics 4A - Chapter 9

Momentum Formula

\overrightarrow{P}=m\cdot\overrightarrow{v}, where p is momemtum

Impulse Derivative Formula

d\left(\overrightarrow{J}\right)=\overrightarrow{F}\left(t\right)dt (deriv of impulse = force)

Impulse Formula

\overrightarrow{J}=\int_{tᵢ}^{tբ}\overrightarrow{F}\left(t\right)dt

F_ave Formula

F\left(ave\right)=\frac{1}{tբ-tᵢ}\int_{tᵢ}^{tբ}F\left(t\right)dt , then F\left(ave\right)=\frac{\overrightarrow{J}}{tբ-tᵢ} or F\left(ave\right)=\frac{\overrightarrow{J}}{\Delta t}

Impulse Momentum Theorem

\overrightarrow{J}=\overrightarrow{P}բ-\overrightarrow{Pᵢ}

Conservation of Linear Momentum Formula Applied to Force

F₁ = -F₂

Conservation of Linear Momentum Formula Applied to Momentum

P_1i + … + P_ni = P_1f + … + P_nf

or >

also P₁ + … + P_n = total momentum

Center of Mass Formula

\overrightarrow{r}\left(\operatorname{cm}\right)=\frac{\left(m\left(1\right)r\left(1\right)+\cdots+m\left(n\right)r\left(n\right)\right)}{M} where M is total mass and r_cm is average position of center of mass

Rocket Propulsion Formula

\Delta v=u\ln\left(\frac{mᵢ}{m}\right) where u = exhaust speed and m is m(t)

Momentum of Ejected Gas

P = m_gV_exhaust, wher m_g is the mass of the gas used

Additional Rocket Formula I Don’t Know How to Explain

Types of Collisions

• Inelastic: 0 < K_f < K_i

• Perfectly Inelastic: 0 = K_f

• Elastic: K_f = K_i

• Explosion: K_f > K_i

In a Perfectly Elastic Collision, V (velocity) = …

V_1i + V_1f = V_2i + V_2f