Question

A 3 kg disk of radius 0.25m is rotating freely at an angular speed of 100 rad/s on a shaft passing through the center of mass of the disk. A 2 kg solid ball of the same radius, initially not rotating, slides down the shaft(the shaft passes through the ball's center of mass) and is coupled to the disk.

Assuming that the rotational inertia of the shaft is negligible,

a) What is the angular speed of the disk-ball combination,

b) How would the answer in (a) change if the ball dropped onto the disk next to the shaft and coupled to the disk?

Answer 1

Mass of disk m=3kg Radius & 0.25m, Wof 100 hadla Mass of solid ball masky (Initially at rest) Moment of Inertig object Disk I ball | Shoft MR²/ 300-2002/ 2 2x2x10-2534 0 (Fg m²) 0.09375 7,10 momentum = 0.09375) (100) (JW) = 9.37514 Initially Final Iz w (4) colore 0.05 Angular | Iwo and "I W Applying conservation of Angular homestum 9.37570 s flit Iz sw's (0.09375+0.05) 9.375 9.375= 0.143756. 2 w = 0.14375 w=65.21 had/ Ball and disk buth rotates on the shaft anys. But rodational inertia of shoftes negligible. Since shaft act as aneis of ratation and all the of dirt on the asun of ratation will be at rest. since any on where on the shoft except the disle surface. The velocity of ball does not charge. Heree velocity of the disk also never charge.