Answer:
The ratio of the skaters final moment of inertia to his initial moment of inertia is 0.338
Explanation:
Moment of inertia = mr^2 = m(v/w)^2 = mv^2/w^2
Initial angular velocity (w) = 3.75 rad/s
Initial moment of inertia = mv^2/3.75^2 = 0.071mv^2
Final angular velocity (w) = 6.45 rad/s
Final moment of inertia = mv^2/6.45^2 = 0.024
Ratio = 0.024/0.071 = 0.338
Answer:
1 : 1.72.
Explanation:
Moment of inertia {\displaystyle I}I is defined as the ratio of the net angular momentum, L of a system to its angular velocity,w around a principal axis.
I = L/w
Given:
w1 = 3.75 rad/s
w2 = 6.45 rad/s
Therefore,
I1 = L1/3.75
= 0.27L1
I2 = L1/6.45
= 0.155L1
At constant momentum, L ratio of the initial moment of inertia to the final moment of inertia =
3.75 I1 : 6.45 I2
= 1 : 1.72.
1.74
