3. Angular Momentum
Figure skaters spend a lot of time rotating through the air or spinning on the ice. They score more when they can spin or rotate faster and longer. To spin faster and longer, the skater must develop a large amount of angular momentum. Angular momentum is the amount that a body is rotating about a point throughout the jump. Angular momentum is generated by the skater applying a force against the ice, then the ice applies a ground reaction force on the skater and this ground reaction force gives the angular momentum.
Angular momentum is represented by the equation L=IW, where I equals the moment of rotational inertia about the spin axis and is equal to 0.5mr^2 where m is mass and r is radius. W represents angular velocity, which means how fast the skater is spinning. The moment of inertia depends on the mass of an object and also the distribution of the mass around the axis of rotation.
The conservation of angular momentum is the principle that the angular momentum of an object remains constant as long as there is no external torque or moment acts on the object. The equation for the conservation of angular momentum is I1W1 (initial) = I2W2 (final). For instance, the moment of inertia decreases, the angular rotation has to increase to keep the same angular momentum. This is evident when a figure skater spins. A skater starts the spin with arms stretched (large moment of inertia). As the skater brings the arms in (decreasing the moment of inertia), the rotational speed increases. This is how those skaters like Mao Asada and Yuna Kim can perform incredible spins and jumps, along with many years of practice.
Question ) What is the angular momentum of a figure skater spinning (with arms close to her body) at 4.4 rev/s, assuming her to be a uniform cylinder with a height of 1.6m, radius of 16cm and mass of 42 kg? ( Answer in kgm^2/s)
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