Physics, 17.12.2020 17:40 Nina0016

A solid disk with a mass of 0.8 kg and a radius of 12cm is rotating at a rate of 2.6 rev/s. Another disk with half the mass and half the radius is dropped on top of the first disk. What is the new angular speed of both disks when they are rotating together?

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Answer from: mawawakaiii

The new angular speed of both disks when they are rotating together is 2.311 revolutions per second.

Explanation:

This situation can be analyzed by the Principle of Conservation of Angular Momentum since there are no external forces and moments being exerted on the system, whose definition is presented below:

$I_{o}\cdot \omega_{o} = I_{f}\cdot \omega_{f}$ (1)

Where:

$\omega_{o}$ , $\omega_{f}$ - Initial and final angular speeds, measured in revolutions per second.

$I_{o}, I_{f}$ - Initial and final moments of inertia, measured in kilograms per square meter.

The initial and final moments of inertia of the system are, respectively:

$I_{o} = \frac{1}{2}\cdot m_{o}\cdot r_{o}^{2}$ (2)

$I_{f} = \frac{1}{2}\cdot \left[m_{o}\cdot r_{o}^{2}+\frac{1}{2}\cdot m_{o}\cdot \left(\frac{1}{2}\cdot r_{o} \right)^{2}\right]$

$I_{f} = \frac{1}{2}\cdot m_{o}\cdot r_{o}^{2}+\frac{1}{16}\cdot m_{o}\cdot r_{o}^{2}$

$I_{f} = \frac{9}{16}\cdot m_{o}\cdot r_{o}^{2}$ (3)

By applying (2) and (3) in (1), we obtain the following expression:

$\frac{1}{2}\cdot m_{o}\cdot r_{o}^{2}\cdot \omega_{o} = \frac{9}{16}\cdot m_{o}\cdot r_{o}^{2}\cdot \omega_{f}$

$\frac{1}{2}\cdot \omega_{o} = \frac{9}{16}\cdot \omega_{f}$

$\omega_{f} = \frac{8}{9}\cdot \omega_{o}$ (4)

If we know that $\omega_{o} = 2.6\,\frac{rev}{s}$ , then the new angular speed of both disks when they are rotating together is:

$\omega_{f} = \frac{8}{9}\cdot \left(2.6\,\frac{rev}{s} \right)$

$\omega_{f} = 2.311\,\frac{rev}{s}$

The new angular speed of both disks when they are rotating together is 2.311 revolutions per second.

Answer from: Quest

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27

Answer from: Quest

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

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