someone help me answer this.

Bug Walking on Pivoted Ring A ring of radius R and mass my lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass my walks on the ring with constant speed v relative to the ring, starting at the pivot, when the ring is initially at rest. Take k to point out of the page. top view frictionless table ring bug Pluot Point (a) What is the angular velocity of the ring when the bug is halfway around? Express you answer in terms of some or all of the following: mi, m2, u, R and k. (b) What is the angular velocity of the ring when the bug is back at the pivot? Express you answer in terms of some or all of the following: mı, m2, v, R and k.

The angular velocity of the ring when the bug is halfway around and the angular velocity of the ring when the bug is back at the pivot is [m₂v / {(2m₁ +m₂)R}].

What is angular velocity?

The velocity of a particle when moving in the circular path.

Let speed of the bug with respect to ground is u.

Speed of bag with respect to ring will be

v = u - (- Rω) =

Then, u = v- Rω...............(1)

Angular momentum of ring and bug will remain conserved.

Initial momentum: L ring + Lbug =0

Final momentum: -2m₁ R²ω + m₂uR =0...............(2)

Using equation (1) and (2), the angular velocity expression will be

ω =[m₂v / {(2m₁ +m₂)R}] in positive z direction

Thus, the angular velocity of the ring when the bug is halfway around and the angular velocity of the ring when the bug is back at the pivot is [m₂v / {(2m₁ +m₂)R}].

Learn more about angular velocity.

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