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Chapter 11: Problem 6

Why does a tetherball move faster as it winds up its pole?

Short Answer

Expert verified
The tetherball moves faster as it winds up its pole due to the conservation of angular momentum. As the ball moves closer to the pole (reducing the radius), its speed increases while its angular momentum remains conserved.

Step by step solution

01

Understanding Circular Motion

To start understanding why the ball gets faster, it's crucial to understand the concept of circular motion. In the case of a tetherball, the circular path gradually decreases as the ball winds around the pole. As the path gets smaller, the speed of the tetherball increases. This is a result of the conservation of angular momentum.
02

Applying the Conservation of Angular Momentum

Angular momentum is given by the equation \( L = mvr \), where \( m \) is mass, \( v \) is velocity (speed), and \( r \) is radius (distance from the pole to the ball). In this case, angular momentum must remain constant since there are no external torques acting on the tetherball. As the radius decreases, the ball's speed must increase for the angular momentum to remain conserved. This explains why the tetherball moves faster as it winds up its pole.

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