Radial or centripetal acceleration is never defined only for circular motion, it may be defined for any type of motion. Radial acceleration is always directed towards the instantaneous center of curvature of the trajectory so it is also named centripetal acceleration. Radial acceleration is always along normal to the instantaneous velocity so it is also known as normal acceleration. Since this component of acceleration is always directed along the radius of curvature of the trajectory (projectile motion), that's why the name radial acceleration is given to this type of acceleration. We must keep in mind that the resultant acceleration is the sum of these two types of accelerations and the formula along with the required figure is stated below:Įquation (4) states that the radial component of acceleration means the component of resultant acceleration which is perpendicular to the instantaneous velocity for the motion along any general path (not necessarily for circular motion). You can see the tangents drawn to the path of the object with the changing velocity. This is for the centripetal or radial acceleration. The below images show the variation of radial acceleration with the tangential acceleration: The tangential acceleration acts tangentially to the path along which the object moves during a circular motion. Now, it is crystal clear that the radial component is the primary reason for any object to keep making a circular motion.Ī body whose acceleration is always directed along the radius as its name signifies, there is one more component of acceleration whenever an object travels with a non-uniform speed and that is tangential acceleration ( a t ). Because of this reason we see that the smaller merry-go-rounds rotate a lot faster than the big ones. However, the centripetal acceleration points radially inwards or towards the center, which is what makes you go round.Īnd from the formula in equation (3), we can see that the greater the radius of the circle of rotation, the lesser is its rate of change of velocity or the radial acceleration and vice-versa. The direction of the velocity vector taken from your position will be tangential to the circular path in which the merry-go-round is making rounds. Let’s suppose that your child is on a merry-go-round. Symbolically, these two units are written as ωs-2 or ms -2 ,respectively. So, we get the radial acceleration formula as:Įquation (3) is called centripetal acceleration. The formula for the centripetal force acting on the stone moving in a circular motion is mv 2 /r….(2) So centripetal force is the reason for a radial acceleration.Ī body whose mass is ‘m’ and the force acting on it is ‘ma r ’.(1) It happens because of the centripetal force. Radial acceleration is symbolized as ‘a r ’ and it is the rate of change of angular velocity whose direction is towards the center about whose circumference, the body moves. So, let’s start with radial acceleration: We know that in a circular motion, the direction of the angular rate of velocity changes with time constantly so that’s why its angular acceleration gets two following components namely: When it is linear motion, we consider just acceleration however, during circular motion, which is actually an angular acceleration. We know that a body can execute two types of motion and they are linear and circular motion. So, do you know what radial acceleration is? Well! When angular velocity changes in a unit of time, it is a radial acceleration. It is measured in ms -2 however, one more term lies in Physics and that is Radial Acceleration. It is a vector quantity that bears both magnitude and direction. Acceleration is nothing but the changing velocity of an object in a unit of time. We know that when a body is subjected to an external force, it starts accelerating and this is what Newton’s second law says.
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