A ballet student with her arms and a leg extended has a moment of inertia of 2.4 kgm^2 as she spins with a rotational speed of 1.0 rev/s. As she draws her arms and a leg in toward her axis of rotation, her moment of inertia becomes 0.60 kgm^s. Determine her final rotational speed.
To determine the final rotational speed of the ballet student, we can use the principle of conservation of angular momentum. According to this principle, the initial angular momentum should be equal to the final angular momentum.
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.
angular momentum is conserved
angular momentum = moment of inertia * rotational speed