Question

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the bottom of the core with a constant speed of 25.0 cm/s, what is the speed of the spool

Answer 1

v₁ = 37.5 cm / s

Step-by-step explanation:

For this exercise we can use that angular and linear velocity are related

v = w r

in the case of the spool the angular velocity for the whole system is constant,

They indicate the linear velocity v₀ = 25.0 cm / s for a radius of r₀ = 1.00 cm,

w = v₀ /r₀

for the outside of the spool r₁ = 1.5 cm

w = v₁ / r₁1

since the angular velocity is the same we set the two expressions equal

`(v_o)/(r_o) = (v_1)/(r_1)`

v1 =
`(r_1)/(r_o) \ \ v_o`

let's calculate

v₁ =
`(1.50)/(1.00) \ \ 25.0`

v₁ = 37.5 cm / s