A student is applying force to a merry-go-round with two other students sitting on the edges. How can the student provide the maximum force to rotate the merry-go-round?
To provide the maximum force to rotate the merry-go-round, the student should apply the force at the maximum distance from the center of rotation. This can be achieved by pushing or pulling on the outer rim of the merry-go-round, as far away from the center as possible. The force applied at a greater distance from the center produces a larger torque, or turning force, which leads to a faster rotation.
To understand why this is the case, we can consider the concept of torque. Torque is the rotational equivalent of force and is calculated by multiplying the force applied by the distance from the axis of rotation. In this scenario, the axis of rotation is the center of the merry-go-round.
Mathematically, the torque (τ) can be calculated using the equation: τ = F × r, where F is the applied force and r is the distance from the center of rotation.
By applying the force at the outer edge of the merry-go-round, the student maximizes the value of r, thus maximizing the torque. This torque helps overcome the inertia of the system and initiates a faster rotation.
Additionally, it's important to note that the direction of the force matters as well. The force needs to be applied tangentially to the circle, perpendicular to the radius, in order to maximize the torque and facilitate rotation.