Disk A, with a mass of 2.0 kg and a radius of 50 cm , rotates clockwise about a
ID: 1785303 • Letter: D
Question
Disk A, with a mass of 2.0 kg and a radius of 50 cm , rotates clockwise about a frictionless vertical axle at 40 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 40 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?
Explanation / Answer
A)
Ia = moment of inertia of disk A = (0.5) (2) (0.50)2 = 0.25 kgm2
wa = 40 rev/s
Ib = moment of inertia of disk B = (0.5) (2) (0.30)2 = 0.09 kgm2
wb = - 40 rev/s
w = angular speed after collision
using conservation of angular momentum
Ia wa + Ib wb = (Ia + Ib) w
(0.25) (40) + (0.09) (-40) = (0.25 + 0.09) w
w = 19 rev/s
b) direction : clockwise