Rotational Motion and Centre of Mass: One-Page Formula Sheet

Rotational Motion and Centre of Mass — formula sheet

Formulas

• I_ring = MR², I_disc = ½MR², I_solid sphere = ⅖MR², I_rod (centre) = ML²/12
• Parallel axis: I = I_cm + Md²
• KE of rolling = ½mv²(1 + k²/R²)
• Acceleration down incline (rolling) = g sinθ / (1 + k²/R²)

Key ideas

• Torque τ = r × F; τ = Iα about a fixed axis
• Angular momentum is conserved when net external torque is zero
• Rolling without slipping: v = ωR
• Parallel and perpendicular axis theorems

Traps to avoid

• Taking torque about a point that is accelerating
• Forgetting static friction in rolling (it does no work but changes motion)
• Mixing up I about the centre and about an edge

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