Rotational Motion
December 8, 2016
Categorised in: 12th Physics
(1) $I = Σ m_i r_i_^2$ (system of particles)
$I = ∫r^2 dm$ (rigid body)
(2) $I = M k^2$
(3) $E_{rot} = 1/2 I w^2$ (Also, subst. w = 2πf)
(4) $E_{rolling} = 1/2 M v^2 (1 + {k^2}/{R^2})$ = $1/2 M v^2 (1 + I/{MR^2})$ = $1/2 M w^2 (R^2 + k^2)$
(5) Rolling down an inclined plane, $v = √{{2gh}/{1 + c}}$ & $a = {g sinθ}/{1 + c}$
Here, h = L sinθ & $c = {k^2}/{R^2}$ = ${I}/{MR^2}$
(6) Work done by constant external torque,
$∆KE_{rot} = 1/2 I (w_2_^2 – w_1_^2)$
(7) $τ = {dl}/{dt}$ => l is conserved if $τ_{ext}$ = 0
(8) τ = I α (~F = ma)
L = I w (~P = mv)
$KE = 1/2 I w^2$ ($~KE= 1/2 m v^2$)
Power = τ w (~Power = F.v)
$\ov L = \ov r x \ov p$
L = mrv (θ = 90°)
(9) $w_{2} = w_{1} + 2as$
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