Name: Motion in a Plane With Constant Acceleration
Uploaded: 2019-07-19
Duration: 6 min 42 s
Description: In this video, we are going to look at the simple concept of motion in a plane with constant acceleration. You'll be able to master the concept in just a few...

Question

What is centripetal acceleration? Derive an expression for it in terms of constant speed of the body.

Accepted Answer

Centripetal acceleration, property of the motion of a body traversing a circular path. The acceleration is directed radially toward the centre of the circle and has a magnitude equal to the square of the body’s speed along the curve divided by the distance from the centre of the circle to the moving body. The force causing this acceleration is directed also toward the centre of the circle and is named centripetal force.

Angular speed ω= $\frac{∆ θ}{∆ t}$

Let $v_{1}$ and $v_{2}$ be the velocity vectors

$ω ∆ t$ = $\frac{|∆ V|}{|V|}$

$= \frac{|∆ V|}{∆ t} = |V| ω = (ω r) ω = ω^{2} r$

or When 𝚫t→0 then $\frac{|∆ V|}{∆ t}$ represents the magnitude of centripetal acceleration at P which is given by $|a| = \frac{|∆ V|}{∆ t} = ω^{2} r (\frac{V^{2}}{r})$

Then $|\vec{a}| = ω^{2} r = \frac{V^{2}}{r}$

Example of centripetal acceleration is a stone moved around tied to the string.

What is centripetal acceleration? Derive an expression for it in terms of constant speed of the body.

Important Questions on Description of Motion in Two and Three Dimensions

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