Question

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?

Answer 1

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

$\omega = \dfrac{2\pi N}{60}$

$\omega = \dfrac{2\pi \times 60}{60}$

ω = 6.28 rad/s

Time taken is t

ω = α₂ t

6.28 = 0.1 t

t= 62.8 s