# Common angular speed after collision

• csimon863
In summary, two disks with equal masses but different radii rotate in opposite directions about a frictionless vertical axle at 30 rev/s. The smaller disk slides down the axle and lands on top of the larger disk, after which they rotate together. The question is what is their common angular speed in rev/s after the collision? The solution involves using conservation of angular momentum and the equation L=Iw, where I is the moment of inertia and w is the angular velocity. The final angular speed is found to be 29.27 rev/s.
csimon863

## Homework Statement

Disk A, with a mass of 9.0 and a radius of 90 , rotates clockwise about a frictionless vertical axle at 30 . Disk B, also 9.0 but with a radius of 10 , rotates counterclockwise about that same axle, but at a greater height than disk A, at 30 . Disk B slides down the axle until it lands on top of disk A, after which they rotate together.

## Homework Equations

ive been trying to find the acceleration? a=delta w/delta t but obviously this isn't wokring!

## The Attempt at a Solution

I can't even attempt a solution. I am completely lost on this one, so much so i registered for physics forum just to get some help.

Whats the question? Edit: I see it now in the heading. What about conservation of angular momenta?

the setup: disk a has a mass of 9.0 kg and a radius of 90cm, rotates clockwise about a frictionless vertical axle at 30 rev/s. disk b, also 9.0 kg but with a radius of 10cm 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. after the collision, what is their common angular speed in rev/s?

i tried:
A has L= I x w, I = mass x rad^2 = 7.29 x -30 = -218.7 L for b = +2.7. So the final L = -216 CW

its not working. very frustrating.

maybe the math--using cm-kg: this is the (1/2 mR^2) x revs/sec
a: +9 x 8100/2 x 30
b: -9 x 100/2 x 30
Sum: 9 x 8000/2 x 30 = 36000 x 30 = 108 x 10^4

Sum for the composite= [9 x 8100/2 + 9 x 100/2] x ? =9 x 4100 x ?
? = 29.27 RPS

PS: clockwise rotation I define as positive quantity.

## 1. What is common angular speed after collision?

Common angular speed after collision refers to the final angular velocity of two objects that collide with each other. It is the same for both objects and is determined by the conservation of angular momentum.

## 2. How is common angular speed after collision calculated?

The formula for calculating common angular speed after collision is ωf = (I1ω1 + I2ω2) / (I1 + I2), where ωf is the final angular velocity, I1 and I2 are the moments of inertia of the two objects, and ω1 and ω2 are their initial angular velocities.

## 3. What factors affect the common angular speed after collision?

The common angular speed after collision is affected by the masses and moments of inertia of the objects, as well as the initial angular velocities and the type of collision (elastic or inelastic).

## 4. Can the common angular speed after collision be greater than the initial angular velocities?

No, the conservation of angular momentum dictates that the total angular momentum before and after the collision must be equal. Therefore, the common angular speed after collision cannot be greater than the initial angular velocities of the two objects combined.

## 5. How does the common angular speed after collision differ from linear speed?

The common angular speed after collision refers to the rotation of objects, while linear speed refers to the movement of objects in a straight line. The two are related, but the common angular speed after collision takes into account the distribution of mass around an axis, while linear speed does not.

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