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Angular velocity is a key concept in understanding rotational motion. It measures how quickly an object rotates around a specified axis. More simply put, it tells us how fast something is spinning.
In mathematical terms, angular velocity is often represented by the symbol \( \omega \). It is calculated using the formula:

• \( \omega = \frac{2\pi}{T} \)

where \( T \) is the period of rotation, or the time taken for one complete circle or cycle. This formula helps us find angular velocity when we know how long it takes for one rotation.
In the case of the ice skaters, they complete one full spin in 2.5 seconds. Using the formula, \( \omega = \frac{2\pi}{2.5} \), we find that their angular velocity is approximately 2.51 rad/s. This means each skater rotates 2.51 radians every second while spinning. Understanding this allows us to further explore forces involved in their circular motion.

Circular motion occurs when an object moves along the circumference of a circle. This kind of motion can be seen in daily life, such as cars going around a roundabout, or indeed, skaters twirling on ice.
Two main forces play a role here: the centripetal force, which keeps an object moving along a curved path, and the centrifugal force, often perceived by the rotating object, which seems to push it outwards.
Centripetal force acts towards the center of the circle and is essential for circular motion. In the case of the skaters, each skater pulls on the other to maintain their circular path. This is achieved by the centripetal force, calculated using:

• \( F_c = m \omega^2 r \)

where \( m \) is the mass, \( \omega \) is the angular velocity, and \( r \) is the radius of the circular path. This formula reveals the force required to keep an object moving in a circle at a constant speed.
For our skaters, substituting \( m = 60 \) kg, \( \omega = 2.51 \) rad/s, and \( r = 0.80 \) m gives us \( F_c = 301.26 \) N. This means each skater exerts approximately 301.26 newtons of force to maintain their spinning motion.

Skaters on ice provide a fascinating example of physics in motion. When two skaters hold hands and spin, they exhibit a real-life demonstration of circular motion and the forces involved. The unique surface of ice, with its low friction, allows skaters to spin with ease.
As they rotate, skaters rely heavily on maintaining balance and using the right amount of force to keep their motion steady. Each skater's arm length essentially becomes the radius of their spinning path. This affects how tightly they can spin and the force needed.
By grasping each other's hands, they create a mutual center of rotation, making it crucial that both apply equal force for smooth motion.

• Ice provides minimal resistance, enhancing their ability to freely rotate while demonstrating principles like conservation of angular momentum.
• More experienced skaters can control their speed and direction by adjusting their arm positions.

Their spins become a perfect mix of muscular strength, understanding of physics, and graceful execution, providing both a challenging sport and a compelling study of motion physics.