Question

a wheel of diameter 3.00 cm has a 4.00 m cord wrapped around its periphery. starting from rest, the wheel is given a constant angular acceleration of 4.00 rad/s2. how long will it take the cord to unwind?

Answer 1

It will take 1 second for the cord to unwind.

Step-by-step explanation:

To find the time it takes for the cord to unwind, we need to determine the angular velocity of the wheel. We can use the equation:

ω = ω0 + αt

Where:

• ω = final angular velocity
• ω0 = initial angular velocity (0)
• α = angular acceleration (4.00 rad/s2)
• t = time

Since the wheel starts from rest, the initial angular velocity (ω0) is 0. Therefore, the equation simplifies to:

ω = αt

Substituting the values we have:

4.00 rad/
`s^2` = 4.00 rad/
`s^2` × t

Solving for t:

t = 1 s

Therefore, it will take 1 second for the cord to unwind.