For a particle in uniform circular motion (radius R and angular velocity ω), the magnitude and direction of acceleration, respectively are
ω2R, towards the centre of the circle
In uniform circular motion, the speed stays constant but the direction of velocity continuously changes, which requires a centripetal (centre-seeking) acceleration.
Using \(v = \omega R\), the centripetal acceleration is \(a = \dfrac{v^2}{R} = \dfrac{(\omega R)^2}{R} = \omega^2 R\), and it is always directed radially inward, towards the centre of the circle, so that the particle keeps curving along the circular path instead of moving off in a straight line.
Hence, the magnitude and direction of the acceleration are ω2R, towards the centre of the circle.
Similar Questions
Velocity (m/s)-time (s) graph is plotted for the motion of two cars A and B for 10 s, when the cars are initially at rest and acquire final velocities as VA and VB, respectively. The respective straight lines of the graph make angles 30° and 60°, respectively with the x-axis (time). The difference in velocities VB and VA is
Important Questions from Motion
The motion of a particle of mass m is described by the relation, y = ut - 1⁄2 gt2, where u is the initial velocity of the particle. The force acting on the particle is
The motion of ______ body is an example of uniformly accelerated motion.
- in a particular direction is velocity.
Motion of an object is if its velocity is constant.
The motion of the body moving along a circular path is an example of ______.
