Answer :
Final answer:
The radius of the flywheel is approximatelyA) 1.38 meters.
Explanation:
To find the radius of the flywheel, we can use the formula for the angular velocity of a rotating object, which is ω = 2πf, where ω is the angular velocity in radians per second and f is the frequency of rotation in revolutions per second. Since the flywheel spins at 397 revolutions per minute (rpm), we need to convert this to revolutions per second by dividing by 60. Then, we can use the formula for linear velocity, v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the flywheel. Solving for r, we find r = v/ω.
First, we need to convert 397 rpm to revolutions per second: 397 rpm / 60 = 6.6167 revolutions per second. Then, we calculate the angular velocity: ω = 2π × 6.6167 = 41.621 radians per second. Next, we rearrange the formula for linear velocity to solve for the radius: r = v/ω. Given that linear velocity is related to the tangential speed of the flywheel, and the tangential speed is related to the radius by v = ωr, we have v = 397 rpm * 2π * r / 60. Solving for r, we have r = v / (397 rpm * 2π / 60).
Substituting the values, we get r ≈ (397 rpm * 2π / 60) / 41.621 ≈ 1.38 meters. Therefore, the radius of the flywheel is approximately 1.38 meters.
So correct option is A) 1.38m
