conservation of momentum
I*5.6=(.31)I wf
wf=5.6/.31 rad/sec
I*5.6=(.31)I wf
wf=5.6/.31 rad/sec
The formula for angular momentum is given by L = Iฯ, where L is the angular momentum, I is the moment of inertia, and ฯ is the angular speed.
Initially, the skater's moment of inertia is I1 and angular speed is ฯ1.
After pulling in his arms, the skater's moment of inertia becomes 0.31 times its original value, or I2 = 0.31 * I1.
Since angular momentum is conserved, we can write: L1 = L2.
L1 = I1 * ฯ1
L2 = I2 * ฯ2
Since L1 = L2, we can set the two equations equal to each other and solve for ฯ2:
I1 * ฯ1 = I2 * ฯ2
Substituting the values we know:
I1 * (5.6 rad/s) = (0.31 * I1) * ฯ2
Simplifying the equation:
5.6 rad/s = 0.31 * ฯ2
Dividing both sides by 0.31:
ฯ2 = (5.6 rad/s) / 0.31
Calculating the result:
ฯ2 โ 18.06 rad/s
Therefore, the figure skater's angular speed after pulling in his arms is approximately 18.06 rad/s.