Newtonian mechanics

• How Does a Screw Fall in an Accelerating Elevator?
  A dropped screw’s motion relative to an elevator depends on the elevator’s acceleration. Use relative acceleration to find its fall time.
• What Is the Relation Between Gravitational Potential and Field?
  Gravitational field is the negative gradient of gravitational potential. Learn the sign, units, point-mass formula, and a worked example.
• What Is the Relation Between Potential Energy and Force?
  For a conservative force, force is the negative slope or gradient of potential energy; see how to calculate it and interpret the sign.
• How Are Impulse and Momentum Related?
  Impulse equals the change in momentum, and it is the time integral of force. A system’s momentum is conserved when its net external impulse is zero.
• Does ABS Shorten a Car’s Stopping Distance?
  ABS often shortens braking distance for ordinary drivers, especially on slippery roads, but it does not always beat expert threshold braking or stop sooner on loose.
• What Is the Derivative of Kinetic Energy?
  The derivative of kinetic energy depends on the variable: with respect to time it is power, and with respect to velocity it is momentum.
• Can Conservative Forces Change a System’s Mechanical Energy?
  A conservative force can change kinetic energy, but its work is offset by an equal change in potential energy when no nonconservative work acts.
• Can Internal Forces Change a System’s Total Momentum?
  Internal forces can redistribute momentum among a system’s parts, but they cannot change its total momentum when the system is isolated.
• Can Magnitude Be Negative?
  Magnitude is never negative: it measures size. Signed quantities such as potential energy or a vector component can be negative, depending on direction or reference.