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What is centripetal acceleration and derive its formula also?
Ref: https://edurev.in/question/702216/What-is-centripetal-acceleration-and-derive-its-formula-also-
A body that moves in a circular motion (of radius r) at constant speed (v) is always being accelerated. The acceleration is at right angles to the direction of motion (towards the center of the circle) and of magnitude v2 / r.
The direction of acceleration is deduced by symmetry arguments. If the acceleration pointed out of the plane of the circle, then the body would leave the plane of the circle; it doesn't, so it isn't. If the acceleration pointed in any direction other than perpendicular (left or right) then the body would speed up or slow down. It doesn't.
Now for the magnitude. Consider the distance traveled by the body over a small time increment Δt:
We can calculate the arc length s as both the distance traveled (distance = rate * time = v Δt) and using the definition of a radian (arc = radius * angle in radians = r Δθ:)
The angular velocity of the object is thus v / r (in radians per unit of time.)
The right half of the diagram is formed by putting the tails of the two v vectors together. Note that Δθ is the same in both diagrams.
FAQs on Deriving the centripetal acceleration formula - Class 11
| 1. How can I derive the centripetal acceleration formula? |  |
Ans. To derive the centripetal acceleration formula, we can start with the basic equation for centripetal acceleration, which is given by a = v^2/r. This equation relates the centripetal acceleration (a) to the velocity (v) and the radius (r) of the circular path. By manipulating this equation and using the definitions of velocity and acceleration, we can derive the centripetal acceleration formula.
| 2. What is the significance of centripetal acceleration? | |
Ans. Centripetal acceleration is important because it describes the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and is responsible for keeping the object in its circular path. Without centripetal acceleration, an object would move in a straight line tangent to the circle instead of following a curved path.
| 3. How does centripetal acceleration differ from tangential acceleration? | |
Ans. Centripetal acceleration and tangential acceleration are both components of the total acceleration of an object moving in a circular path. Centripetal acceleration is directed towards the center of the circle and is responsible for changing the direction of motion. Tangential acceleration, on the other hand, is directed tangent to the circle and is responsible for changing the speed of the object. While centripetal acceleration always exists in circular motion, tangential acceleration may or may not be present, depending on whether the object's speed is changing.
| 4. Can centripetal acceleration ever be zero? | |
Ans. No, centripetal acceleration cannot be zero as long as an object is moving in a circular path. Centripetal acceleration is a result of the object's velocity changing direction, and even if the object is moving at a constant speed, it will still experience centripetal acceleration. The only way for centripetal acceleration to be zero is if the object is not moving in a circular path but is instead moving in a straight line.
| 5. How does centripetal acceleration relate to centripetal force? | |
Ans. Centripetal acceleration and centripetal force are closely related. According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In the case of circular motion, the net force acting on the object is the centripetal force, which is directed towards the center of the circle. Therefore, the centripetal force can be calculated using the formula F = ma, where a is the centripetal acceleration. In this way, centripetal acceleration provides a link between the motion of an object and the force required to keep it moving in a circular path.
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