Question

The angular velocity of a point on a circle with a radius of 8 feet is 10π radians per second. What is the speed of the point?

1) 80 π ft/sec
2) 0.8 π ft/sec
3) 1.25 π ft/sec

Answer 1

The speed of the point on the circle with a radius of 8 feet and an angular velocity of 10π radians per second is 80π ft/sec.

Step-by-step explanation:

The student has asked to determine the speed of a point on a circle with a known radius and angular velocity. The formula to find the linear speed (v) is given by v = r⋅ω, where 'r' is the radius of the circle and 'ω' (omega) is the angular velocity. In this case, with r = 8 feet and ω = 10π radians per second, we can calculate the speed as follows:

Speed (v) = Radius (r) × Angular Velocity (ω)

Speed (v) = 8 ft × 10π rad/sec

Speed (v) = 80π ft/sec

Therefore, the correct answer is 1) 80π ft/sec.