Kinetic Energy and Momentum Relations

A set of vocabulary-style flashcards defining the mathematical relationships between Kinetic Energy, mass, velocity, and momentum as presented in the lecture notes.

$$KE = \frac{1}{2}mv^2$$

The core formula for Kinetic Energy where $m$ stands for mass and $v$ stands for velocity.

$$KE \propto m$$

The relationship where Kinetic Energy is directly proportional to mass when velocity ($v$) is constant, expressed as $\frac{K_1}{K_2} = \frac{m_1}{m_2}$.

$$KE \propto v^2$$

The relationship where Kinetic Energy is directly proportional to the square of velocity when mass ($m$) is constant, expressed as $\frac{K_1}{K_2} = \frac{v_1^2}{v_2^2}$.

$$KE = \frac{p^2}{2m}$$

The formula relating Kinetic Energy ($KE$) to momentum ($p$) and mass ($m$).

$$p = \sqrt{2mKE}$$

The formula for calculating momentum ($p$) when the Kinetic Energy ($KE$) and mass ($m$) are known.

$$KE \propto p^2$$

The relationship where Kinetic Energy is directly proportional to the square of momentum when mass ($m$) is constant.

$$KE \propto \frac{1}{m}$$

The relationship where Kinetic Energy is inversely proportional to mass when momentum ($p$) is constant, represented by the ratio $\frac{K_1}{K_2} = \frac{m_2}{m_1}$.

$$F = \frac{2KE}{r}$$

A derived formula relating force ($F$) to Kinetic Energy ($KE$) and a variable $r$, resulting from the expression $KE = \frac{1}{2}Fr$.