A woman stands at the center of a platform. The woman and the platform rotate with an angular speed of 4.00 rad/s. Friction is negligible. Her arms are outstreched, and she is holding a dumbbell in each hand. In this position the total moment of inertia of the rotating system (platform, woman, and dumbbells) is 5.40kg.m2. By pulling in her arms, she reduces the moment of inertia to 4.40kg*m2. Find her new angular speed.
Apply the law of conservation of angular momentum.
I1*w1 = I2*w2
I2/I1 is the moment of inertia ratio. It equals w1/w2. Solve for w2.
w1 = 4.00 rad/s
To find the woman's new angular speed, we'll use the law of conservation of angular momentum. According to this law, the initial angular momentum of a system should be equal to the final angular momentum.
The initial angular momentum is calculated by multiplying the initial moment of inertia (I1) by the initial angular speed (w1). In this case, I1 is given as 5.40 kg*m^2 and w1 is given as 4.00 rad/s.
So, the initial angular momentum is I1 * w1 = 5.40 kg*m^2 * 4.00 rad/s = 21.60 kg*m^2/s.
We're also given the final moment of inertia (I2), which is 4.40 kg*m^2. We need to find the new angular speed (w2).
Using the law of conservation of angular momentum, we can set up the equation:
I1 * w1 = I2 * w2
Substituting the values we know:
(5.40 kg*m^2) * (4.00 rad/s) = (4.40 kg*m^2) * w2
Simplifying the equation:
21.60 kg*m^2/s = 4.40 kg*m^2 * w2
Dividing both sides by 4.40 kg*m^2:
(21.60 kg*m^2/s) / (4.40 kg*m^2) = w2
The units of kg*m^2 cancel out, leaving us with:
w2 = 21.60 kg*m^2/s / 4.40 kg*m^2 ≈ 4.91 rad/s
Thus, her new angular speed is approximately 4.91 rad/s.