A uniform disc of mass m and radius R rotates about a fixed vertical axis passing through its centre with angular velocity ω. A particle of same mass m and having velocity 2 ωR towards centre of the disc collides with the disc moving horizontally and sticks to its rim the angular velocity of the disc is ω/n. Find n.
Physics · Rotational Motion · angular momentum in pure rotation and its conservation
JEE Advanced

Question

A uniform disc of mass m and radius R rotates about a fixed vertical axis passing through its centre with angular velocity ω. A particle of same mass m and having velocity 2 ωR towards centre of the disc collides with the disc moving horizontally and sticks to its rim the angular velocity of the disc is ω/n. Find n.

Physics · Rotational Motion · angular momentum in pure rotation and its conservation

G1 Physics · Accepted Answer

Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives 3.