A uniform circular disc placed on a rough horizontal surface has initially a velocity v₀ and an angular velocity ω₀ as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then v₀ /rω₀ is

Question

G1 Physics · Accepted Answer

Kinetic friction gives translational deceleration a=µg and angular deceleration α=2µg/r for a uniform disc because I=½mr². For both translation and rotation to stop at the same instant, v₀/(µg)=ω₀/(2µg/r). Therefore v₀/(rω₀)=1/2, which is option A.