A puck on a horizontal, frictionless surface is attached to a string that wraps around a pole of finite radius, as shown in the figure .

As the puck moves along the spiral path, does its speed increase, decrease, or stay the same?

angular momentum remains constant because no torque.

Therefore speed increases and radius decreases.

To determine whether the speed of the puck increases, decreases, or stays the same as it moves along the spiral path, we need to consider the forces acting on the puck.

Since the surface is frictionless, the only force acting on the puck is the tension in the string. This tension provides the centripetal force necessary to keep the puck moving in a circular path.

As the puck moves along the spiral path, the radius of the circle it travels decreases. The tension in the string, therefore, needs to increase to provide the required centripetal force.

According to Newton's second law, the centripetal force is given by the equation F = (mv^2)/r, where F is the centripetal force, m is the mass of the puck, v is the speed of the puck, and r is its distance from the center of the circle.

Since the mass of the puck remains constant and the radius is decreasing, for the centripetal force to remain constant, the speed of the puck must increase. This means that as the puck moves along the spiral path, its speed increases.

In summary, as the puck moves along the spiral path, its speed increases due to the decreasing radius of the circular path, which requires a higher speed to maintain constant centripetal force.

As the puck moves along the spiral path, its speed decreases. This is because the string wrapping around the pole causes the effective radius of the path to decrease as the puck moves towards the center. According to the law of conservation of angular momentum, the product of radius and angular momentum must be constant. Since the radius decreases, the angular momentum must increase, which results in a decrease in speed.