A wheel has a 32 inch diameter. The speed of a point on its rim is 44 ft/sec. What is its angular speed?
To determine the angular speed of a wheel, you need to understand the relationship between linear speed (in this case, 44 ft/sec) and angular speed. Angular speed is typically measured in radians per second (rad/s).
To find the angular speed, you can use the formula:
Angular speed (in rad/s) = linear speed (in ft/sec) / radius (in ft)
First, you need to find the radius of the wheel using the given diameter of 32 inches. The radius is half the diameter, so the radius of the wheel is:
Radius = 32 inches / 2 = 16 inches
Since the linear speed is given in ft/sec, you need to convert the radius from inches to feet by dividing it by 12:
Radius in feet = 16 inches / 12 = 4/3 feet
Now, plug in the values into the formula to calculate the angular speed:
Angular speed = 44 ft/sec / (4/3 feet)
Angular speed = 44 ft/sec * (3/4 feet)
Angular speed = 33 ft/sec
Therefore, the angular speed of the wheel is 33 rad/s.