Circular Motion and Gravitation

Period (T)

The time it takes for an object to travel once around the circle, calculated as T = 2πr/v.

Centripetal Acceleration (ac or arad)

The acceleration directed towards the center of the circle, with a magnitude of v^2/r, responsible for changing the direction of velocity in circular motion.

Newton's Second Law (Circular Motion)

States that a net external force is necessary to produce centripetal acceleration in uniform circular motion, with the acceleration directly proportional to the net force and inversely proportional to mass.

Centripetal Force (Fc)

The net force required to keep an object moving on a circular path, which always points towards the center of the circle.

Object Released from Circular Path

When the radial (centripetal) force on an object vanishes, it moves straight at a constant velocity, following Newton's first law.

Static Friction (Centripetal Force)

The force between a car's tires and the road that provides the necessary centripetal force to keep the car on a flat curved road without skidding.

Safe Driving Speed (Flat Curve)

The maximum speed a car can safely navigate a flat curve, dependent on the static friction coefficient (μs), gravitational acceleration (g), and radius (r), given by v = sqrt(μs * g * r).

Frictionless Banked Curve

A curved road designed such that the horizontal component of the normal force provides the entire centripetal force, allowing a car to navigate it without friction at a specific ideal speed (v = sqrt(rg * tanθ)).

Car Speed < Ideal (Banked Curve)

If a car's speed is less than the ideal speed on a banked curve, friction acts up the incline to prevent the car from sliding down towards the center of the turn.

Car Speed > Ideal (Banked Curve)

If a car's speed is greater than