Answer:
ω3 = 31.15 rad/s
Explanation:
given data
mass = 1 kg
radius = 2 m
spinning = 45 rad/s
mass = 2 kg
radius = 3 m
spinning = 25 rad/s
solution
we get here first moment of inertia that is express as
I(1) = 0.5 × M1 × r1² .............1
put here value that is
I(1) = 0.5 × 2 × 2² = 4
and
moment of inertia of disk 2nd is
I(2) = 0.5 × M2 × r2² .............2
I(2) = 0.5 × 2 × 3² = 9
so we get here angular momentum that is express as
I(1) ω1 + I(1) ω2 = ( I(1) + I(2) ) ω3
put here value and we get
4 × 45 + 9 × 25 = ( 4 +9 ) ω3
ω3 = 31.15
Answer:
12.27 rad/s
Explanation:
Moment of inertia = mass x radius^2
For disk 1 = 1 x 2^2 = 4 kg-m^2
For disk 2 = 2 x 3^2 = 18 kg-m^2
Rotational momentum = moment of inertia x angular speed
For disk 1 = 4 x 45 = 180 rad-kg-m/s
For disk 2 = 18 x (-25) = -450 rad-kg-m/s.
Total rational momentum of the system = 180 - 450 = -270 rad-kg-m/s.
The minus means the total rotational momentum is 270 rad-kg-m/s in the direction of disk 2.
According to conservation of angular momentum, initial momentum of system must equal the final momentum of system.
Final momentum of system = total moment of inertia of the system times the new angular velocity of system.
= (4 + 18) x Wf = 22Wf
Equating both moment we have,
22Wf = 270
Wf = 270/22 = 12.27 rad/s
