Angular Speed Calculation: How Fast Can a Skater Spin?

What is Angular Speed?

What is the concept of angular speed and how is it related to linear speed?

Angular Speed Explanation

Angular speed refers to the rate at which an object rotates around a fixed point, measured in radians per second (rad/s). It is closely connected to linear speed, which is the actual speed a point on the object's edge travels. Angular speed is calculated by dividing the linear speed by the radius of the rotational motion.

When a skater spins, her hands have both angular and linear speed. The angular speed determines how quickly the skater rotates, while the linear speed indicates how fast her hands move through space as she spins.

Understanding Angular Speed Calculation

Angular speed is defined as the angle traversed by a rotating object in a unit of time, typically measured in radians per second. The formula to calculate angular speed is ω = V/r, where ω represents angular speed, V represents linear speed, and r represents the distance from the center of rotation.

In the case of the skater spinning at 180 rpm with her hands 140 cm apart, the calculation involves converting the distance to meters and then using the formula to determine the linear speed of her hands:

Given radius (r) = 140 cm / 2 = 70 cm = 0.7 m

Angular speed (ω) = 140 rpm = 140 rotations per minute = 140 rotations / 60 seconds = 2.33 rotations per second

Linear speed (V) = ω * r = 2.33 rad/s * 0.7 m = 1.63 m/s

Therefore, the speed of the skater's hands when they are 140 cm apart is 1.63 m/s.