Question

relation between linear and angula varibles in vector form ​

Answer 1

Explanation:

Linear Angular

Variables: x, t, v, and a

v = Δx / Δt.

a = Δv / Δt ; a = ( vf - vi ) / Δt.

x = (1/2) a t2 + vi t.

vf2 - vi2 = 2 a x.

Variables: θ, t, ω, and α

ω = Δθ / Δt.

α = Δω / Δt ; α = ( ωf - ωi ) / Δt.

θ = (1/2) α t2 + ωi t.

ωf2 - ωi2 = 2 α θ.

Table 1

The Relations between Linear and Angular Variables:

Each of the angular variables θ, ω, and α is related to its corresponding linear variable x, v, and at by factor R, the radius of rotation.

x = Rθ ; v = Rω ; at = Rα . (at means tangential acceleration).

This can be easily verified by the following simple mathematics:

Starting with s = Rθ, or x = Rθ and writing as Δx = RΔθ, and then dividing both sides by Δt, yields:

Δx/Δt = RΔθ/Δt ; the left side is v and the right side is ω ; therefore, v = Rω.

If v = Rω is divided through by Δt , yields:

Δv/Δt = R Δω/Δt ; the left side is at and the right side is α ; therefore, at = Rα.

Hope you understand

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