Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.270 rev/s. The magnitude of the angular acceleration is 0.896 rev/s². Both the angular velocity and angular accleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.720 mm . Compute the fan's angular velocity magnitude after time t= 0.196s has passed.

Keep 3 digits after the decimal point, in revolutions per second rev/s.

Answer 1

The fan's angular velocity magnitude after 0.196 s is approximately 0.446 rev/s.

Step-by-step explanation:

To find the angular velocity magnitude after a specific time has passed, we can use the equation:

ω = ω₀ + αt

where ω is the final angular velocity magnitude, ω₀ is the initial angular velocity magnitude, α is the angular acceleration magnitude, and t is the time.

Plugging in the given values, we have:

ω = 0.270 rev/s + (0.896 rev/s²)(0.196 s)

Calculating this expression gives us the final angular velocity magnitude:

ω ≈ 0.270 rev/s + 0.176 rev/s

ω ≈ 0.446 rev/s

Therefore, the fan's angular velocity magnitude after 0.196 s is approximately 0.446 rev/s.