Final answer:
To calculate the angular velocity of a wheel turning at 150 rev/min in radians per second, convert rev/min to rev/s and multiply by 2π to get 5π rad/s.
Step-by-step explanation:
To find the angular velocity of the wheel in radians per second when it turns at 150 rev/min, we can use the formula ω = 2π × (number of revolutions per second). Firstly, convert revolutions per minute to revolutions per second by dividing by 60, as there are 60 seconds in a minute. This gives 150/60 = 2.5 rev/s. Since there are 2π radians in one revolution, the angular velocity in radians per second will be 2π × 2.5 = 5π rad/s. Thus, the angular velocity of the wheel is 5π radians per second.