Two disks of identical mass but different radii (r and 2r) are spinning on frictionless bearings at the same angular speed ?0, b

Question

3 years ago

5

Two disks of identical mass but different radii (r and 2r) are spinning on frictionless bearings at the same angular speed ?0, b

ut in opposite directions. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular velocity.a) what is there final angular speed?b) what is the change in the rotational kinetic energy?

Physics

1 answer:

cestrela7 [59] · Answer 1 · 2022-03-04T23:59:29+03:00

Answer:

Explanation:

Moment of inertia of a disc = 1/2 M R²

Since mass is same for both and radius are r and 2r, their moment of inertia can be in the ratio of 1: 4 . Let them be I and 4I . Angular speed are ω₀ and - ω₀ .

We shall apply law of conservation of angular momentum .

initial total angular momentum

I x ω₀ - 4I x ω₀ = - 3Iω₀

Let final common angular momentum be ω

total final angular momentum = ( I + 4I ) ω

Applying law of conservation of angular momentum

( I + 4I ) ω = - 3Iω₀

ω = - 3 / 5 ω₀ .

b )

Initial total rotational K E

= 1/2 I ω₀² + 1/2 4I ω₀²

= 1/2 x5I ω₀²