An ice skater, has a rotational inertia of I = 4 kg m2, and spins at 2 rad/sec. She then changes her rotational inertia to 2 kg m2. What is her final angular velocity?

a. 4 rad/s
b. 2 rad/s
c. 2.8 rad/s
d. 8 rad/s

The answer must be A then right.

No, the answer is not A. To solve this problem, we can use the principle of conservation of angular momentum. According to this principle, the initial angular momentum (L_initial) is equal to the final angular momentum (L_final) in the absence of any external torques.

The angular momentum (L) is given by the equation: L = I * ω, where I is the rotational inertia and ω is the angular velocity.

Given that the initial rotational inertia (I_initial) is 4 kg m^2 and the initial angular velocity (ω_initial) is 2 rad/s, we can calculate the initial angular momentum (L_initial) as follows:
L_initial = I_initial * ω_initial = 4 kg m^2 * 2 rad/s = 8 kg m^2/s.

Since there is no external torque acting on the skater, the initial angular momentum (L_initial) is conserved.

Now, when the rotational inertia changes to 2 kg m^2, the final angular inertia (I_final) becomes 2 kg m^2. To find the final angular velocity (ω_final), we can use the equation: L_final = I_final * ω_final.

Since the initial and final angular momenta are the same, we can equate them:
L_final = L_initial = 8 kg m^2/s.

Substituting the values, we get:
I_final * ω_final = 8 kg m^2/s.

Plugging in I_final = 2 kg m^2, we have:
2 kg m^2 * ω_final = 8 kg m^2/s.

Simplifying the equation, we find:
ω_final = 8 kg m^2/s / 2 kg m^2 = 4 rad/s.

Therefore, the correct answer is:

a. 4 rad/s

To find the final angular velocity of the ice skater, we can use the conservation of angular momentum formula:

I1 ω1 = I2 ω2

Where:
- I1 is the initial rotational inertia of 4 kg m2
- ω1 is the initial angular velocity of 2 rad/s
- I2 is the final rotational inertia of 2 kg m2 (given)
- ω2 is the final angular velocity (what we need to find)

Rearranging the formula, we can solve for ω2:

ω2 = (I1 ω1) / I2

ω2 = (4 kg m2 * 2 rad/s) / 2 kg m2
ω2 = 8 rad/s

Therefore, the final angular velocity of the ice skater is 8 rad/s. So the correct answer is option d.