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
I say B, am i right?
No, of course not. Angular momentum is conserved. You reduced the moment of interia (rotational inertia is a really bad term), so angular velocity has to change.
so its A then right
To find the final angular velocity, we can use the principle of conservation of angular momentum. According to this principle, the initial angular momentum must be equal to the final angular momentum.
The formula for angular momentum is L = I * ω, where L is the angular momentum, I is the rotational inertia, and ω is the angular velocity.
Let's calculate the initial angular momentum:
Li = Ii * ωi
= 4 kg m^2 * 2 rad/s
= 8 kg m^2/s
Now, we can use the conservation of angular momentum to find the final angular velocity:
Lf = If * ωf
Since the ice skater changes her rotational inertia to 2 kg m^2, we have:
Lf = 2 kg m^2 * ωf
Since the initial and final angular momenta must be equal:
Li = Lf
Plugging in the values:
8 kg m^2/s = 2 kg m^2 * ωf
Simplifying the equation:
ωf = (8 kg m^2/s) / (2 kg m^2)
= 4 rad/s
Therefore, the final angular velocity is 4 rad/s, so the correct answer is a. 4 rad/s.