We started the unit by learning about tangential velocity and rotational velocity. My class found out that rotational velocity is about the number of rotations over a time. When talking about rotational inertia we discovered that if, for example, two kids are playing on a merry-go-round regardless of their position their rotational velocity is the same! So, does that mean their tangential velocity is the same? No! Tangential velocity depends on how far away the body is from the axis of rotation. If the body is far away from the axis of rotation it needs to cover a greater distance per rotation therefore it has a greater tangential velocity, the opposite is true for an object close to the axis of rotation.
tangential speed ~ radial distance x rotational speed
Rotational inertia:
Rotational inertia is the same as linear inertia but for rotating objects. Just like objects moving in a linear path, rotating objects do not want to stop doing what they are already doing. Rewriting Newton's first law we can say:
An object rotating about an axis tends to remain rotating around an axis unless interfered with by some external force and an object not rotating wants to remain that way unless an outside force is applied.
Rotational inertia depends on concentration of mass and how far is it from the axis of rotation. The furthest away the concentration of mass is from the center the greater it's rotational inertia is. I struggled to convince myself that the greater the rotational inertia the hardest it is to start rotating, I always wanted to say that it would start rotating sooner than an object with a small rotational inertia. The secret to understand this concept is always to remind yourself that the inertia is laziness and the lazier the object is the more reluctant it would be to start rotating!
The video above shows that because the hoop has it's concentration of mass away from the axis and the disk is solid (both have the same mass). The hoop has more rotational inertia and therefore is more reluctant to start rotating and therefore loses the race.
Torque:
After talking about rotational inertia we talked about torque which changes the rotation of things. It is important to know that torque is lever arm times the force (force = weight). The concept of torque is used to understand why some things are balanced and how to create a balanced system. The best example for this is a see-saw. If you have too people with different weights it is impossible to maintain the board balanced if they are both sited the same distance from the axis of rotation since for a system to be balanced there needs to be equal torques. To make the board balanced with different weights you need to increase the lever arm (lever arm = smallest distance from the axis of rotation) of the person with the least weight so that the torques equal. In practice the heaviest person of a see-saw needs to sit close to the center while the lightest one sits away from it
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