Angular Velocity Calculation in Rotational Motion

What is the speed of a skater's hands if they are spinning at 180 rpm with their arms 140 cm apart?

Speed Calculation:

The linear speed of the skater's hands when spinning at 180 rpm with arms 140 cm apart is approximately 13.2 m/s.

To calculate the speed of the skater's hands, we first need to convert the rotational speed from rpm to radians per second. We do this by using the formula: ω = 2πf, where f is the frequency in Hz. Given that the skater is spinning at 180 rpm, we convert this to Hz by dividing by 60 (180/60 = 3 Hz). Therefore, ω = 2π * 3 = 6π rad/s ≈ 18.85 rad/s.

Next, we determine the radius of the skater's arms, which is half of 140 cm (70 cm or 0.7 m). The linear speed of the skater's hands can be calculated by multiplying the angular speed (ω) by the radius (r). Substituting the values, we get: speed = 18.85 rad/s * 0.7 m ≈ 13.2 m/s.

Therefore, the speed of the skater's hands when they are spinning at 180 rpm and their arms are 140 cm apart is approximately 13.2 m/s. This calculation involves the concepts of rotational motion, angular velocity, and linear speed in physics.