Asmall rubber wheel drives the rotation of a larger pottery wheel by running along its edge. the small wheel radius is 1.2 cm, and it accelerates at 3 rad/s2. the pottery wheel has a radius of 36 cm. what is the angular acceleration of the pottery wheel? how long till the pottery wheel rotates at 60 rpm?

α₂= 0.1  rad/s²

t= 62.8 s

Explanation:

Given that

For small wheel

r₁= 1.2 cm

α₁ = 3 rad/s²

For large wheel

r₂= 36 cm

Angular acceleration = α₂  rad/s²

The tangential acceleration for the both wheel will be same

a = α₁ r₁=α₂ r₂

Now by putting the values in the above equation

α₁ r₁=α₂ r₂

3 x 1.2 = 36 x α₂

α₂= 0.1  rad/s²

Given that

N = 60 rpm

Angular speed in rad/s ω

ω = 6.28 rad/s

Time taken is t

ω = α₂ t

6.28 = 0.1 t

t= 62.8 s

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.