JEEGenie
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JEE + NEET
Both exams
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JEE Main · Rotational Motion
A uniform rod of length L and mass M is pivoted at one end and released from rest, horizontal. Find its angular acceleration at the instant of release.
  1. Genie  What actually produces the angular acceleration here?
    The weight Mg, acting at the centre
    The normal force at the pivot
    Step 1Weight acts at L/2
  2. Genie  Right. So the torque about the pivot is —
    τ = Mg · L
    τ = Mg · (L/2)
    Step 2τ = MgL/2
  3. Genie  And a rod about its END, not its centre — which moment of inertia?
    I = ⅓ ML²
    I = 1/12 ML²
    Step 3I = ML²/3
  4. Genie  Put them together. α = τ / I gives you —
    α = 3g / 2L
    α = 2g / 3L
    Step 4α = (MgL/2) ÷ (ML²/3)
  5. You solved it
    α = 3g / 2L

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