angular momentum is conserved
angular momentum = moment of inertia * rotational speed
angular momentum = moment of inertia * rotational speed
The formula for angular momentum is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity (rotational speed).
Let's use subscripts "i" and "f" to denote the initial and final values respectively.
Given:
Moment of inertia (initial), Ii = 2.4 kgm^2
Moment of inertia (final), If = 0.60 kgm^2
Angular velocity (initial), ωi = 1.0 rev/s
Using the principle of conservation of angular momentum, we can write:
Ii * ωi = If * ωf
Plugging in the values:
2.4 kgm^2 * 1.0 rev/s = 0.60 kgm^2 * ωf
Calculating:
2.4 rev = 0.60 kgm^2 * ωf
Dividing both sides by 0.60 kgm^2:
ωf = (2.4 rev) / (0.60 kgm^2)
ωf = 4 rev/s
Therefore, the final rotational speed of the ballet student is 4 rev/s.