SUMMARY

Centripetal Acceleration

**DYNAMICS**

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Centripetal Acceleration

Uniform circular motion emphasizes that velocity vector is constant – but the direction of this constant velocity is not constant.

By definition, acceleration is the change in velocity over time. The “change in velocity” for an object in UCM is the change in the velocity vector.

The acceleration that occurs is toward

the center of the circle. It is the force

that is pulling the object “in”

The centripetal acceleration (the acceleration toward the center of a circle) of an object depends on the velocity of the object and the radius of the circle and is expressed as:

An aeroplane of mass 30000 kg travels a horizontal loop of radius 10 m at the rate of 1000 km/hr. Calculate the centripetal acceleration.

Example:

Example:

A car of 1500 kg tied to the rope of 7 m whose other end is located at the center. If the car is moving at the rate of 5 m/s . Calculate the Centripetal force acting on it?

Solution:

What is DYNAMICS and

UNIFORM CIRCULAR MOTION?

DYNAMICS is a branch of physical science and subdivision of mechanics that is concerned with the motion of material objects in relation to the physical factors that affect them: force, mass, momentum, energy.

When an object is experiencing

UNIFORM CIRCULAR MOTION, it is traveling in a circular path at a constant speed. If r is the radius of the path, and we define the period, T, as the time it takes to make a complete circle, then the speed is given by the circumference over the period. A similar equation relates the magnitude of the acceleration to the speed:

of Uniform Circular Motion

Circular motion in which the speed is constant is called

uniform circular motion.

A

centripetal acceleration

…

occurs whenever a moving object changes direction

does not change the speed of an object

acts at right angles to the velocity at any instant

is directed toward the center of a circle

A

centripetal force

…

is the force that makes a moving object change direction.

is not a particular force, but the name given to the net force responsible for circular motion.

acts at right angles to the velocity at any instant.

is directed toward the center of a circle.

Directions in circular motion:

Velocity is tangential (lies on a tangent to the path).

Centripetal acceleration and centripetal force are radial (point toward the center of a circle).

Centripetal acceleration and velocity are always perpendicular.

Centripetal force and centripetal acceleration are always parallel.

Centripetal Force

Centripetal force (from Latin centrum "center" and petere "to seek") is a force that makes a body follow a curved path: its direction is always orthogonal to the velocity of the body, toward the fixed point of the instantaneous center of curvature of the path. Centripetal force is generally the cause of circular motion.

In simple terms, centripetal force is defined as a force which keeps a body moving with a uniform speed along a circular path and is directed along the radius towards the centre. Isaac Newton's description was: "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre."

The Centripetal force formula is given by

Where m = mass of the moving body,

V = Velocity with which it is moving,

r = radius of circular path.

The Centripetal force is due to the Centripetal acceleration and is given by

Where ac is the Centripetal acceleration and is given by

Note: The Centripetal force is expressed in Kg*m/s^2 or N.

Derivation of Centripetal Force Formula