Centripetal acceleration:
When a particle moves in a circle,an acceleration acts towards the centre which changes the direction of its linear velocity.This acceleration is called normal
accelerationor centripetal acceleration (ar).
Centripetal or radial or normal acceleration
\(
a_N = \frac{{V^2 }}
{r} = r\omega ^2 = v\omega = \frac{{4\Pi ^2 r}}
{{T^2 }} = 4\Pi ^2 n^2 r
\)
Normal acceleration or centripetal acceleration changes the direction of linear velocity only but not its magnitude.
1.Without centripetal acceleration a particle can not move along a circle.
2.In nonuniform circular motion,angular velocity and linear velocity both change.Here direction and magnitude of linear velocity change.
3.A particle in non uniform circular motion will have variable speed and variable velocity
4.In uniform circular motion, tangential acceleration is zero (i.e., at=0)
5.In non unifrom circular motion am acceleration acts on the particle to change the magnitude of its linear velocity.This acceleration is called tangential acceleration(at)
6.Tangential acceleration \(
a_t = r\alpha = r\frac{{\left( {\omega _2 - \omega _1 } \right)}}
{t}
\) .
7.For a body in non uniform circular motion,
Resultant acceleration \(
a = \sqrt {a_N ^2 + a_t^2 } ,i.e.,a = \sqrt {(r\omega )^2 + \left( {r\alpha } \right)^2 }
\).
8.A particle moving along circular path may or may not have tangential acceleration but it should have normal acceleration.
9.A particle in non uniform circular motion will have two accelerations acting on it which are at right angles to each other.
10.When a body is in uniform circular motion in a horizontal plane, its speed,angular velocity,period of rotation, kinetic energy and angular momentum are constant.
11.When a body is in uniform circular motion,in a horizontal plane ,its linear velocity,linear momentum,centripetal acceleration,centripetal force are variable.
12.When a body is in uniform circular motion,tangential acceleration and tangential force work done by centripetal force are zero.
13.When a body is in non unifrom circular motion in horizontal plane,its potential energy is constant .Its speed,linear velocity,angular momentum,linear momentum,kinetic energy,centripetal acceleration tangential acceleration are variable.