Introduction:

How does the rotational motion of an object start? How does its angular velocity change? If you have a cylindrical box and you want to make it rotate around itself, all you need to do is wrap a thread around it and pull it with force, causing it to rotate. The greater the force with which you pull the thread, the faster its rotational speed becomes. In this case, two forces affect the box: gravitational force and tension in the thread. Gravitational force affects the center of the box (you will understand the reason later), while the tension in the thread affects the outer edge of the box, with the force direction perpendicular to the line connecting the center of the box and the point where the thread touches the surface of the box, moving away from it.

Article Elements:

1. Rotational Dynamics:

As you've learned, the force acting on a point mass changes its directed linear velocity, while for a non-point mass, like a fixed cylindrical box, the effect of force changes its directed angular velocity in a specific way. Consider the case of opening a closed door; you exert force to open it, but what is the easiest way to open the door? The key is to obtain the greatest effect when applying the least possible force. To achieve this, the point where the force is applied should be as far as possible from the axis of rotation. In the case of a door, the rotational axis is vertical, passing through the door hinges. The point of force application is the door handle, located on the outer side of the door. To ensure an effective force effect, the force is applied to the door handle (away from the hinges) at a right angle to the door. Both the magnitude and direction of the force, as well as the distance between the axis and the point of force application, determine the change in angular velocity, forming a vector diagram.

2. Lever Arm:

When applying a certain force, the change in directed angular velocity depends on the lever arm, which is the vertical distance from the axis of rotation to the point of force application. If the force is perpendicular to the radius of rotation, as in the case of a cylindrical box, the lever arm equals the distance from the axis, and if not perpendicular, the vertical component of the force is considered. The force applied by the thread around the box is perpendicular to the radius of the box, and if the applied force is not perpendicular, the lever arm's magnitude decreases. To find the lever arm, extend the force vector until it forms a right angle with the line extending from the center of rotation, making the distance between the intersection point and the axis the lever arm. Using trigonometry, the length of the lever arm L can be found with the equation r sin θ =, where r is the distance between the axis of rotation and the point of force application, and θ is the angle between the applied force and the radial line.

3. Torque:

Abdul Rahman wants to enter a stationary revolving door and clarify how the door pushes to generate torque with the least amount of applied force. Where should the point of force application be? Torque measures the ability of force to cause rotation, and its magnitude equals the product of force and the length of its lever arm. Because force is measured in Newtons and distance in meters, torque is measured in Newton-meters (N.m) and represented by the Latin letter τ. It is expressed by the equation τ = Fr sin θ.

4. Finding Net Torque:

In the following experiment, take two pencil erasers, metal coins, transparent tape, and attach two identical coin pieces at the ends of one pencil, letting it balance on top of the other pencil, as shown in figure 5-2. Each coin piece exerts torque equal to its weight and F multiplied by the distance from the balance point to the coin center, according to τ = Fg r. Since the torques are equal in magnitude and opposite in direction, the net torque is zero.

τ1 + τ2 = 0 or Fg1 r1 – Fg2 r2 = 0

Now, how do you make the pencil rotate? You must add another coin piece above one of the existing coin pieces, making the forces different. You can also shift the balance point toward one of the coin pieces, making the distances different.

Conclusion:

1. It is evident that rotational motion depends on several factors, including the applied force and the lever arm. Gravitational force and tension in the thread in the case of a cylindrical box serve as examples of interacting forces affecting rotational motion. In the case of a fixed and non-point mass, the effect of force on angular velocity changes.

2. We understand the importance of the lever arm in altering angular velocity and how to optimize force usage for the greatest effect with the least force. The article also illustrates how to find the net torque when multiple forces act, with the net torque being the sum of the torques.

3. In the final experiment, two pencil erasers and coin pieces were used to illustrate the effect of different forces on torque and rotational motion. By moving the balance point or adding an extra coin piece, torque changes, leading to rotational motion.

4. This understanding of rotational dynamics demonstrates how we can control the motion of rolling objects and enhance the efficiency of the applied forces. This knowledge proves valuable in various fields of life, whether in engineering design, aviation, or understanding the natural motion of objects in the universe.

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