Disk A, with a mass of 2.0 kg and a radius of 60 cm , rotates clockwise about a
ID: 2032805 • Letter: D
Question
Disk A, with a mass of 2.0 kg and a radius of 60 cm , rotates clockwise about a frictionless vertical axle at 30 rev/s . Disk B, also 2.0 kg but with a radius of 30 cm , rotates counterclockwise about that same axle, but at a greater height than disk A, at 30 rev/s . Disk B slides down the axle until it lands on top of disk A, after which they rotate together.
a) After the collision, what is magnitude of their common angular velocity (in rev/s)? Express your answer using two significant figures.
b) In which direction do disks rotate after the collision? Clockwise or counterclockwise?
Explanation / Answer
(a) Moment of inertia of disk A, Ja = (1/2)*m(A)*R^2 = (1/2)*2*0.6^2 = 0.36 kgm^2
For disk B, Jb = (1/2)*2*0.3^2= 0.09 kgm^2
La = ?a*Ja
Lb = ?a*Jb
L = La-Lb = ?a(Ja-Jb) = 2PI*n*0.27 = 6.282*30*0.07 = 13.19 kgm^2/sec
?f = L/(Ja+Jb) = 13.19/0.45 = 0.366*4 = 29.31 rad/sec
So, nf = ?f/(2PI) = 29.31 / 6.28 = 4.67 rev/s.
(b) Direction of the disk after collision shall be in the clockwise direction (the one with major L).