# The Incredible Speed of a Spinning Skater

## What is the speed of a skater's hands as she spins at 150 rpm with her arms outstretched 155 cm apart?

How fast are her hands moving considering the radius of her rotation and the rate at which she spins?

## Calculating the Speed of the Skater's Hands

The skater holds her arms outstretched as she spins at 150 rpm, with her hands 155 cm apart. Given the radius of half of 155 cm, we calculate the circumference of her rotation, which is 486.95 cm. Since she rotates 150 times per minute, she completes 2.5 rotations per second. Multiplying the circumference by the rotation rate, we get 1217.375 cm per second, or approximately 1.22 meters per second.

When a skater spins with her arms outstretched, the speed of her hands can be calculated by considering the radius of her rotation and the rate at which she spins. In this scenario, the skater's hands are 155 cm apart, which gives us the radius for the circle of rotation (half of 155 cm).

To find the circumference of the rotation, we use the formula C = 2 x π x Radius. Substituting the radius value, we get C = 2 x 3.14 x 77.5 ≈ 486.95 cm. This is the distance her hands travel in one complete rotation.

Since the skater spins at 150 rpm (rotations per minute), we need to convert this to rotations per second. Dividing 150 by 60 seconds gives us 2.5 rotations per second.

By multiplying the circumference by the rotation rate, we find that her hands are moving at a speed of 1217.375 cm per second. This translates to approximately 1.22 meters per second, showcasing the impressive velocity of her spinning motion.