5) A flywheel whose angular acceleration is constant and equal to 2.50rad/s^2 rotates through an angle of 100 rad in 5 .00 s. What was the angular velocity of the flywheel at the beginning of the 5.00 s interval? 13.75rad/s

Here's how to solve this problem:<br /><br />**1. Understand the given information:**<br /><br />* Angular acceleration (α) = 2.50 rad/s² (constant)<br />* Angular displacement (θ) = 100 rad<br />* Time (t) = 5.00 s<br /><br />**2. Identify the relevant equation:**<br /><br />We can use the following equation of rotational motion:<br /><br />θ = ω₀t + (1/2)αt²<br /><br />Where:<br /><br />* θ is the angular displacement<br />* ω₀ is the initial angular velocity<br />* α is the angular acceleration<br />* t is the time<br /><br />**3. Solve for the initial angular velocity (ω₀):**<br /><br />We are given θ, α, and t, and we need to find ω₀. Let's rearrange the equation:<br /><br />ω₀ = (θ - (1/2)αt²) / t<br /><br />**4. Plug in the values and calculate:**<br /><br />ω₀ = (100 rad - (1/2)(2.50 rad/s²)(5.00 s)²) / (5.00 s)<br />ω₀ = (100 rad - 31.25 rad) / 5.00 s<br />ω₀ = 68.75 rad / 5.00 s<br />ω₀ = 13.75 rad/s<br /><br />**Answer:**<br /><br />The angular velocity of the flywheel at the beginning of the 5.00 s interval was 13.75 rad/s.<br />