KE = (1/2)mv^2
- Always >= 0 (mass and v^2 are non-negative)
- Scalar quantity
- Frame-dependent (different observers measure different KE)
- Dimension: [ML^2T^{-2}]
KE-Momentum Relation: p = mv, so KE = p^2/(2m) or p = sqrt(2mKE)
Useful Deductions:
- For same KE: p_1/p_2 = sqrt(m_1/m_2) — heavier body has more momentum
- For same momentum: KE_1/KE_2 = m_2/m_1 — lighter body has more KE
- If p is doubled, KE becomes 4 times
- If KE is doubled, p becomes sqrt(2) times
Percentage Change: If v increases by n%, KE increases by approximately 2n% (for small n). Exact: KE_new/KE_old = (1 + n/100)^2