Laws of Motion

A body remains at rest or in uniform motion unless acted upon by a net external force.

Net force equals rate of change of momentum. For constant mass: F = ma.

Every action has an equal and opposite reaction. Forces always occur in pairs.

Momentum is mass times velocity. A vector quantity in the direction of velocity.

Impulse equals force times time, and equals the change in momentum.

Total momentum of a system is conserved when no net external force acts.

Static friction adjusts up to a maximum to prevent relative motion.

Maximum static friction just before the body begins to slide.

Friction force on a body already in motion. Always less than limiting friction.

Friction opposing rolling motion. Much smaller than sliding friction.

Angle between the normal reaction and the resultant contact force when sliding occurs.

Maximum angle of incline at which a body remains stationary without sliding.

Acceleration of a body sliding down a frictionless inclined plane.

Acceleration of a body sliding down a rough inclined plane.

Minimum force needed to move a body on a rough horizontal surface, applied at optimal angle.

Angle at which applied force should be directed to minimise the effort needed to move a body.

Acceleration and tension when force F pulls two bodies connected by a string on a smooth surface.

Two masses over a pulley. Acceleration and tension in terms of the two masses.

One mass on a smooth surface, one hanging. Acceleration and tension.

Acceleration and tensions when force F pulls three bodies connected in a line on a smooth surface.

Force required to keep a body moving in a circular path. Directed toward the centre.

Banking angle for a road so that a vehicle needs no friction to navigate the curve.

Speed limits on a banked road with friction before the vehicle skids.

A mass on a string tracing a horizontal circle. Period and angular velocity.

Minimum speed needed at the top of a vertical circle to maintain tension in the string.

Minimum speed at the bottom needed to complete a full vertical circle.

Tension in the string at angle φ from the vertical during circular motion in a vertical plane.

Fictitious force in a non-inertial (accelerating) reference frame. Opposite to frame acceleration.

Apparent weight increases when lift accelerates up, decreases when accelerating down. Zero in free fall.