Disk A, with a mass of 9.0kg and a radius of 50cm , rotates clockwise about a fr
ID: 2245582 • Letter: D
Question
Disk A, with a mass of 9.0kg and a radius of 50cm , rotates clockwise about a frictionless vertical axle at 20rev/s . Disk B, also 9.0kg but with a radius of 40cm , rotates counterclockwise about that same axle, but at a greater height than disk A, at 20rev/s . Disk B slides down the axle until it lands on top of disk A, after which they rotate together.
Part A
After the collision, what is their common angular speed (in rev/s)?
Express your answer using two significant figures.
Part B
And in which direction do they rotate?
Points will be rewarded to the first correct answer! Thank you :)
Explanation / Answer
Angular momentum of Disk A = I?
?a = 2? Na = 2? * 20 = 40?
?b = 2? Nb = 2? * 20 = 40?
Ia = mr2/2= 9 * 0.5*0.5/2 = 1.125 units
Ib = mr2/2= 9 * 0.4*0.4/2 = 0.72 units
Finally
(Ia +Ib) ? = Ia?a + Ib?b
=> 1.125 ? = (1.125 * 40 - 0.72 *40 )?
=>? = 45.216 radian/sec
w = 7.16 rev /s
Direction is direction of disk A i.e Clockwise