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MHT CET 2025 (23 Apr, Shift 2) · Rotational Kinematics & Dynamics

Rotational Kinematics & Dynamics question from MHT CET 2025 (23 Apr, Shift 2)

Q13MHT CET 2025 · 23 APR · SHIFT 2Easy

Rotational Kinematics & Dynamics

What is the linear velocity if angular velocity ω⃗=3i^−4j^+k^\vec{\omega} = 3\hat{i} - 4\hat{j} + \hat{k} and radius r⃗=(5i^−6j^+6k^)\vec{r} = (5\hat{i} - 6\hat{j} + 6\hat{k})?

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Answer: (c)

  1. v⃗=ω⃗×r⃗\vec{v} = \vec{\omega} \times \vec{r} with ω⃗=(3,−4,1)\vec{\omega} = (3, -4, 1), r⃗=(5,−6,6)\vec{r} = (5, -6, 6)
  2. i^:(−4)(6)−(1)(−6)=−18\hat{i}: (-4)(6) - (1)(-6) = -18
  3. j^:−[(3)(6)−(1)(5)]=−13\hat{j}: -[(3)(6) - (1)(5)] = -13
  4. k^:(3)(−6)−(−4)(5)=2\hat{k}: (3)(-6) - (-4)(5) = 2
  5. So the answer is (c) −18i^−13j^+2k^-18\hat{i} - 13\hat{j} + 2\hat{k}.
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