A high school cheerleader has a baton that is 1 meter long with a 100 gram mass on each end. Another cheerleader has a baton that is 0.5 meter long with the same mass on each end. Neglecting the mass of the rod holding the masses together, which baton will be easier to spin when grasped at the center?

A. The longer baton because it has more mechanical advantage due to a longer lever arm.
B. The shorter baton because it requires less force to move the mass at the end.
C. The shorter baton because it requires less torque.
D. Both batons will be just as easy to spin since the mass of the rod is negligible

To determine which baton will be easier to spin, we need to consider the concepts of mechanical advantage, force required, torque, and the effect of the mass of the rod.

First, let's understand mechanical advantage. Mechanical advantage refers to the factor by which a machine amplifies the force applied to it. It is calculated as the ratio of the output force to the input force. In this case, the batons can be considered as simple machines, where the input force is the force applied to spin the baton and the output force is the rotational motion created.

Second, let's consider the force required. When spinning the baton, the force applied at the center will generate a torque. Torque is calculated by multiplying the applied force by the distance from the point of rotation to the line of action of the force. In this case, the distance is the length of the baton, and the point of rotation is the center of the baton.

Now, let's go through each option to find the correct answer:

A. The longer baton because it has more mechanical advantage due to a longer lever arm.
Mechanical advantage is related to the distance of the force from the point of rotation. In this case, the longer baton does have a longer lever arm, which means the distance from the point of rotation to the force is greater. Therefore, option A is a valid answer.

B. The shorter baton because it requires less force to move the mass at the end.
While it is true that a shorter baton requires less force to move the mass at the end, this option does not take into account the fact that the force required to spin the baton depends on torque, not just the force applied. Therefore, option B is not a complete explanation.

C. The shorter baton because it requires less torque.
This option correctly states that torque is a crucial factor in determining the force required to spin the baton. As the length of the baton decreases, the torque required to rotate it decreases. Therefore, option C is a valid answer.

D. Both batons will be just as easy to spin since the mass of the rod is negligible.
Option D does not consider the effect of torque and only focuses on the mass of the rod. While the mass of the rod does have an impact on the total mass, it is not the sole determinant of the ease of spinning the baton. Therefore, option D is not a complete explanation.

From the explanations provided, we can see that both option A and option C are valid. Therefore, the correct answer could be either:

A. The longer baton because it has more mechanical advantage due to a longer lever arm.
C. The shorter baton because it requires less torque.

Both explanations accurately describe why one baton may be easier to spin than the other.