A small 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?

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Netta00 Netta00 · Answer 1 · 2019-12-03T09:47:57+01:00

Answer:

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

[tex]\omega = \dfrac{2\pi N}{60}[/tex]

[tex]\omega = \dfrac{2\pi \times 60}{60}[/tex]

ω = 6.28 rad/s

Time taken is t

ω = α₂ t

6.28 = 0.1 t

t= 62.8 s