A skate dancer spins about a vertical axis at
1rev/s with arms out Stretched.with her arms
folded,her moment of inertia about the
vertical axis decreased by 60%,Calculate the
rate of revolution...
Plz show step
Inew = .4*I
Inew * omega new = I omega
omega new = (I/.4I) * 1 rev/s
omega new = 1/.4 = 2.5 rev/s
To calculate the rate of revolution, we need to apply the law of conservation of angular momentum. According to this law, the total angular momentum before and after any changes should remain constant.
Let's denote the initial rate of revolution as ω1 (1 rev/s in this case) and the final rate of revolution as ω2 (which we need to find).
The angular momentum (L) of a rotating object is given by the product of its moment of inertia (I) and its angular velocity (ω). Mathematically, L = Iω.
Before folding her arms, the skater dancer has an initial angular momentum (L1) given by L1 = I1 * ω1.
We are given that the moment of inertia (I) decreases by 60% when her arms are folded. So, the final moment of inertia (I2) is equal to 40% (or 0.4) of the initial moment of inertia (I1).
Now, let's calculate the final angular momentum (L2) when her arms are folded. L2 = I2 * ω2.
According to the law of conservation of angular momentum, the initial angular momentum (L1) should be equal to the final angular momentum (L2). Therefore, we can set up the equation:
L1 = L2
I1 * ω1 = I2 * ω2
Since we have the relationship between the two moments of inertia (I1 and I2), we can substitute these values into the equation:
I1 * ω1 = (0.4 * I1) * ω2
Now, we can solve for ω2:
ω2 = (I1 * ω1) / (0.4 * I1)
ω2 = ω1 / 0.4
ω2 = (1 rev/s) / 0.4
ω2 = 2.5 rev/s
Therefore, the rate of revolution when the skater dancer's arms are folded is 2.5 rev/s.