A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 2.0 cm and accelerates at the rate of 7.5 rad/s2, and it is in contact with the pottery wheel (radius 25.0 cm) without slipping. (a) Calculate the angular acceleration of the pottery wheel. in rad/s2 (b) Calculate the time it takes the pottery wheel to reach its required speed of 75 rpm. in seconds

a) α₂ = 0.6 rad / s², b) t = 13.1 s

Explanation:

a) This is an angular kinematics exercise. Let's analyze the situation when the two wheels are in contact and without sliding between them the linear speed is the same. Let's write your expressions

Rubber wheel v₁ = w₁ r₁

Ceramic wheel v₂ = w₂ r₂

v₁ = v₂

w₁ r₁ = w₂ r₂

w₂ = w₁ r₁ / r₂

We use the angular kinematic equation for the rubber wheel

w₁ = w₀ + alf₁ t

w₁ = α₁ t

we replace

w₂ = r₁ / r₂ (α₁ t)

w₂ = 0.020 / 0.25 7.5 t

w₂ = 0.6 t

therefore,

α₂ = 0.6 rad / s²

b) let's reduce to the SI system

w₂ = 75 rpm (2π rad / 1 rev) (1min / 60s) = 7.854 rad / s

We clear the equation and calculate

t = w₂ / alf₂

t = 7.854 / 0.6

t = 13.1 s