Final answer:
The angular frequency can be determined by converting the change in angular velocity to radians per second and then dividing by the time interval. For an example calculation, a one-fourth revolution change over 0.0150 seconds results in an approximate angular frequency of 105 rad/s.
Step-by-step explanation:
To find the angular frequency in rad/s with a single digit of precision, you need to consider the information provided where Δw (change in angular velocity) is 250 revolutions per minute (rpm) and Δt (time) is 5.00 seconds. First, convert the angular velocity to radians per second (rad/s) by using the conversion factor that there are 2π radians in one revolution and 60 seconds in one minute. Then, use the angular frequency formula ω = ΔΘ/Δt, where ΔΘ is the change in angle in radians.
For example, calculating the angular frequency for a change of one-fourth of a revolution in 0.0150 seconds is done as follows: (π/2) rad / 0.0150 s = 104.7 rad/s, which is approximately 105 rad/s with single-digit precision.