Why does a ballet dancer spin faster when pulling in their arms?

A ballet dancer spins faster when pulling in their arms due to the principle of conservation of angular momentum.

Concept Explanation:

Angular momentum is given by:
L = I × ω

Where:

• L = angular momentum (constant if no external torque acts)
• I = moment of inertia
• ω = angular velocity (speed of rotation)

What Happens During the Spin:

• When the dancer stretches their arms outward:
• The moment of inertia (I) is large
• The angular velocity (ω) is smaller
• When the dancer pulls their arms inward:
• The moment of inertia decreases
• To keep angular momentum constant, angular velocity increases

Key Insight:

Since L remains constant, any decrease in I must result in an increase in ω.
This is why the dancer spins faster.

Real-Life Analogy:

This principle is also observed in:

• Ice skaters spinning faster when pulling in arms
• Planets moving faster when closer to the sun (in orbital motion context)

Conclusion:

A ballet dancer spins faster when pulling in their arms because reducing the moment of inertia increases angular velocity, maintaining constant angular momentum.