A ceiling fan with 20-in. blades rotates at 50 rpm.
(a) Find the angular speed of the fan in rad/min.
(b) Find the linear speed of the tips of the blades in in./min.
Incorrect: Your answer is incorrect.
in/min
To find the angular speed of the fan in rad/min, we need to convert the given 50 rpm to rad/min.
Since there are 2π radians in one revolution, we can multiply the given rpm by 2π to convert it to rad/min.
Angular speed = 50 rpm x 2π rad/rev = 100π rad/min.
Therefore, the angular speed of the fan is 100π rad/min.
To find the linear speed of the tips of the blades in in./min, we need to use the formula:
Linear speed = angular speed x radius.
Since the radius of the blades is 20 inches, we can plug in the values:
Linear speed = 100π rad/min x 20 inches = 2000π inches/min.
Therefore, the linear speed of the tips of the blades is 2000π inches/min.