AI Tutor
Catching a 95 mph fastball barehanded stings painfully, but catching the exact same ball with a padded glove feels effortless.
The incoming ball loses the exact same velocity in both cases, so what makes the glove so much safer?

Momentum: Mass in Motion

Linear momentum (symbolized by p⃗\vec{p}) is the product of an object's mass and its velocity: p⃗=mv⃗\vec{p} = m\vec{v}.
Because velocity has direction, momentum is a vector quantity measured in kilogram-meters per second (kgβ‹…m/s\text{kg}\cdot\text{m/s}).
How do forces change this quantity of motion over time?

The Impulse-Momentum Theorem

In 1687, Isaac Newton formulated his Second Law of Motion as the rate of change of momentum over time: F⃗net=Δp⃗Δt\vec{F}_{\text{net}} = \frac{\Delta \vec{p}}{\Delta t}.
Multiplying both sides by Δt\Delta t gives impulse (J⃗\vec{J}), which states that J⃗=F⃗avgΔt=Δp⃗\vec{J} = \vec{F}_{\text{avg}}\Delta t = \Delta \vec{p}.
Notice that 1Β Nβ‹…s=1Β (kgβ‹…m/s2)β‹…s=1Β kgβ‹…m/s1\text{ N}\cdot\text{s} = 1\text{ (kg}\cdot\text{m/s}^2)\cdot\text{s} = 1\text{ kg}\cdot\text{m/s}, confirming impulse and momentum share identical units.
What happens when the collision force isn't constant, but spikes and drops rapidly like a real bat hitting a ball?