if angular momentum is conserved
Initialangulmomentum=I*w
= I*4
final angular momentum=
1/2 I * wf=I*4
wf=8 rad/sec
Initialangulmomentum=I*w
= I*4
final angular momentum=
1/2 I * wf=I*4
wf=8 rad/sec
The angular momentum (L) of an object is given by the product of its moment of inertia (I) and its angular velocity (ω): L = Iω.
Initially, the skater has a certain angular momentum (L1) with a moment of inertia (I1) and an angular speed (ω1). We can write this as L1 = I1ω1.
When the skater changes the position of her arms, the moment of inertia of her body decreases to one half its initial value, i.e., I2 = 0.5I1.
According to the conservation of angular momentum, L1 = L2. Rewriting this equation in terms of moment of inertia and angular velocity, we get I1ω1 = I2ω2.
Substituting the values, we have:
I1ω1 = (0.5I1)ω2.
Simplifying the equation, I1 cancels out:
ω1 = 0.5ω2.
Now we can solve for ω2, which is the final angular speed:
ω2 = 2ω1.
Given that ω1 = 4 rad/s, we can substitute this value to find ω2:
ω2 = 2(4) = 8 rad/s.
Therefore, the skater's final angular speed is 8 rad/s.