IIT (NTSE/Olympiad)  

Circular Motion & Rotational Dynamics

6. Equation of linear motion and rotational motion

6. Equation of linear motion and rotational motion
(i) With constant velocity a = 0, s = ut α = 0, θ = ωt
(ii) With constant acceleration (i) Average velocity
vav=
(ii) Average acceleration
aav=
(iii) s = vav t = t
(iv) v = u + at
(v) s = ut + at2
(vi) s = vt – at2 (vii) v2 = u2+ 2as
(viii) Sn = u + (2n – 1)a
displacement in nnhsec

(i) Average angular velocity
wav=
(ii) Average angular acceleration
aav =
(iii) q = wav. t = t
(iv) ω2= ω1 + αt
(v) θ = ω1t + at2
(vi) θ = ω2t – αt2
(vi) ω22 = ω12 + 2α θ
(viii) θn= ω 1 + (2n – 1)α
Angular displacement in nnhsec

(iii) With variable acceleration (i) v =
(ii) ds = v dt
(iii) a = = v
(iv) dv = a dt
(v) v dv = a ds

(i) ω = dθ/dt
(ii) dθ = ωdt
(iii) α = = ω
(iv) dω = α dt
(v) ω dω = α dθ



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