![]() ![]() Moreover, we get angular velocity or ω simply by dividing normal velocity by the radius of the circular path. Since centripetal acceleration is of a body in a circular path, angular velocity matters here. So, if you are a high-school student in physics, you already know that in rotational dynamics, omega or ω stands for angular velocity. Centripetal acceleration formula in terms of omega However, there is another way to express it. The key to this is the knowledge of similarity in triangles. So, this is how we derive the centripetal acceleration formula. Moreover, we also know that Δs/ Δt is velocity or v. Now, we already know that Δv/ Δt gives the acceleration which in this case is ac. Now, if we divide the entire equation by Δt, we get. Hence, let us first solve the expression to get Δv. Moreover, if we apply the theorems of similar triangles here, we will get. Therefore, the two equal sides of the velocity vector triangle are the speeds v1 = v2 = v. Moreover, if you look closely you will see that the triangle that the velocity vectors form and the one that the radii r and Δs form are similar. So, we already know that the direction of centripetal acceleration is toward the center of curvature, but we need to find its magnitude. We will see the derivation of the centripetal acceleration formula in reference to this figure. Are radial and centripetal acceleration the same?Ĭentripetal acceleration formula derivation.Is centripetal acceleration always positive?.What is the relationship between centripetal force and acceleration?.Does centripetal acceleration depend on speed?. ![]()
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