Question

What is centripetal acceleration? Derive its formula. A particle

executes 4 revolutions per second on a circular path of radius

0.25 meter. Find centripetal acceleration of the particle.​

Answer 1

Answer:

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Answer 2

Answer: Centripetal acceleration is a characteristic property of an object's motion along a circular path. Centripetal acceleration applies to any object travelling in a circle with an acceleration vector pointing in the direction of the circle's centre.

Explanation: When a body is travelling along a curve, the total distance from the circle's centre to the moving body is divided by the acceleration that is applied radially in the direction of the curve's centre, with a magnitude equal to the square of the body's speed. Centripetal force is the name given to the force that accelerates and is pointed in the direction of the circle's centre.

Mathematically,   $a = v^{2} /r$

where, a  is the centripetal acceleration

            v is the velociy

           r is the radius in m.

For a particle executing 4 revolutions per second on a circular path of radius 0.25 m. The centripetal acceleration can be given as;

given n = 4 rev/s

angular velocity $w =2n$

                               = 8 rad/s

we know,   $w =v/r$

substituting in the formula of centripetal acceleration,

angular velocity=32 pirad/s

                        a = (( 32 * 3.14)^2) / 0.25

                           = 157.75 m/s^2