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Solution
R = u² sin 2θ / g34.6 m
Ball at 20 m/s, 30° — find range
  • 1Draw the path
  • 2Range formula
  • 3Put the values
AnswerR ≈ 34.6 m
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1. Angular Momentum✓ 01:15
2. Parallel Axis ThmCurrent
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F = G · (m₁m₂ / r²)
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τ = r × F = Iα
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ROTATIONAL_DYNAMICS_Q42.mp4
Audio: Hinglish + English4K 60fps
Doubtclip Engine • Step 2 of 4
Step 2: Conservation of Angular Momentum
I₁ω₁ + I₂ω₂ = (I₁ + I₂) · ω_final

Since no external torque acts about the central pivot axis (∑τ_ext = 0), the total angular momentum of the disc-rim system is strictly conserved. We substitute the parallel-axis moment I = I_cm + Md² before the disc fully embeds.

01:42 / 03:15
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Solution Milestones

3 steps total
✓
00:00 - Question Formulation
Free body diagrams and isolated boundary setup.
2
01:15 - Moment of InertiaActive
Application of parallel axis theorem: I = I_cm + Md²
3
02:40 - Numerical Substitution
Final angular velocity & kinetic energy loss ratio.
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