a skater with moment of inertia 15 kgm2 begins a spin with an angular speed of 6.0 rad/s by changing the position of her arms, the skater decreases her moment of inertia by 50% what is the skaters final angular speed
To find the skater's final angular speed, we need to apply the law of conservation of angular momentum. The formula for angular momentum is given by:
L = Iω
Where:
L = Angular momentum
I = Moment of inertia
ω = Angular speed
Initially, the skater's moment of inertia is 15 kgm^2 and the angular speed is 6.0 rad/s. Let's calculate the initial angular momentum (L_initial) using these values:
L_initial = I_initial * ω_initial
= 15 kgm^2 * 6.0 rad/s
= 90 kgm^2/s
Now, the skater decreases her moment of inertia by 50%. This means the new moment of inertia (I_final) will be half of the initial moment of inertia.
I_final = 0.5 * I_initial
= 0.5 * 15 kgm^2
= 7.5 kgm^2
Now, we need to find the final angular speed (ω_final). We can rearrange the formula for angular momentum to solve for ω:
L_final = I_final * ω_final
Since angular momentum is conserved, we know that L_final should be equal to L_initial:
L_initial = L_final
Substituting the values, we have:
I_initial * ω_initial = I_final * ω_final
Solving for ω_final:
ω_final = (I_initial * ω_initial) / I_final
= (15 kgm^2 * 6.0 rad/s) / 7.5 kgm^2
= 12 rad/s
Therefore, the skater's final angular speed is 12 rad/s.