Physics · Classical Mechanics
A particle is moving in space with O as the origin. Some expressions for its position, velocity, and acceleration in cylindrical coordinates (ρ, φ, z) are given below. Which one of these is NOT correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Angular momentum along z is conserved if ρ(d2φ/dt2) + 2(dρ/dt)(dφ/dt) = 0
- 2Acceleration a = (d2ρ/dt2 − ρ(dφ/dt)2) uρ + ρ(d2φ/dt2) + ((d2φ/dt2) + 2(dρ/dt)(dφ/dt)) uφ + (d2z/dt2) uz✓
- 3Velocity vector v = (dρ/dt) uρ + ρ (dφ/dt) uφ + (dz/dt) uz
- 4Position vector r = ρ uρ + z uz
Correct answer
Acceleration a = (d2ρ/dt2 − ρ(dφ/dt)2) uρ + ρ(d2φ/dt2) + ((d2φ/dt2) + 2(dρ/dt)(dφ/dt)) uφ + (d2z/dt2) uz
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