Question

uniform rod of length L rotating with an angular velocity Omega while its Centre moves with a velocity V is equal to omega l by 6 if the end of the rod is suddenly fixed the angular velocity of rod will be​

Answer 1

Given:

• Length of rod = L
• Angular velocity = ω
• Velocity of centre = V/6

To find:

Angular Velocity of rod when one end is suddenly fixed (ω)

Solution:

• By applying Law of conservation of momentum,
• Iω + mvl/2 = ml²ω'/3
• For a rod, I = ml²/12 and v=ωl/6
• ∴ ml²ω/12 + m ω l²/12 = ml²ω'/3
• ml² is present in each term so it gets cancelled.
• ω'/3 = ω/12 + ω/12
• ω' = 3*2*ω/12
• ∴ ω'= ω/2

Answer:

• If the end is suddenly fixed, angular velocity will be ω/2 i.e. omega/2.