Final answer:
To determine the time it takes for the cord to unwind from a wheel with a radius of 2 cm and a length of 4 m given a constant angular acceleration of 1 rad/s², we calculate that it will take 20 seconds for the cord to completely unwind.
Step-by-step explanation:
The question involves calculating the time it takes for a cord to unwind from the periphery of a wheel that is given a constant angular acceleration starting from rest. The wheel has a radius of 2 cm, and the length of the cord is 4 m. To find the unwinding time, we need to use equations of rotational motion. Since the angular acceleration (α) is given as 1 rad/s², we can relate the angular displacement (θ), which is equivalent to the length of the cord divided by the radius of the wheel, to the angular acceleration and time using the following equation:
θ = αt²/2
Accordingly, the length of the cord (θr) is 4 m, and the radius (r) is 0.02 m, resulting in an angular displacement (θ) of 200 rad (since 4 m / 0.02 m = 200). We can solve for time (t) as follows:
200 = (1 × t²)/2
t² = 400
t = 20 seconds
Therefore, the cord will take 20 seconds to fully unwind from the wheel.