Question

A wheel of diameter 8.0 cm has a cord of length 6.0 m wound around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 3.0 rad/s2. How long will it take the cord to unwind?

Answer 1

Answer: time t = 10s

Step-by-step explanation:

Given;

Diameter = 8.0cm = 0.08m

Radius r = diameter/2 = 0.08/2 = 0.04m

Cord length d = 6.0m

Angular acceleration = 3.0rads/s2

Time = t

Converting the angular acceleration to linear acceleration

a = a* × r = 3.0 × 0.04 = 0.12m/s

d = vt + 1/2 (a × t^2)

Initial velocity v = 0, vt = 0 therefore;

d = 1/2 ( a × t^2)

t = √(2d/a)

t = √ [(2× 6)/0.12]

t = 10s