Unitl 4 Summary

In Unit 4, our main focus was Rotation.  We learned just about everything about the hows and whys of rotation, contributing to our greater understanding of not only Physics but also the world around us.

TANGENTIAL AND ROTATIONAL VELOCITY

An important differentiation to make is that between Tangential and Rotational Velocity.  Tangential Velocity is the velocity we have talked about in previous units- it is the amount of distance covered in a period of time.  Rotational speed is the number of times something completes a circle, and is measured in RPMs, or Rotations per minute.  The two are inversely proportional.  It is possible for an object to have both Rotational velocity and Tangential velocity.

For Example:
Gears have a CHANGING Rotational velocity, but the CONSISTENT Tangential velocity.

Train wheels have CONSTANT Rotational velocity, but CHANGING Tangential velocity.


Train Wheels are a great example for this unit.  They are designed with a wider inner rim and a more narrow outer rim.  This causes the wheels to have the same rotational  velocity (as they are both completing the same number of RPMs), but the outer rim has a faster Tangential velocity, as it is covering the more distance in a given time. This design means that if the train begins to drift off to one side, the faster tangential speed of the outer rim will cause the train to curve toward the middle part of the track, self correcting.

Rotation Inertia is the property of an object that resists changes in spin and motion.  The amount of rotational inertia in an object is dependent of the location of the objects mass in relation to the object's axis of rotation.  An object with MORE rotational rotational inertia is HARDER to spin, while an object with LESS rotational inertia is EASIER to spin.

Below is a great video that demonstrates Rotational Inertia.

ROTATIONAL/ANGULAR MOMENTUM

Along the lines of Rotational Inertia is Rotational/Angular Momentum.  This is the law, similar to the Law of Conservation of Mass, which states that:

Angular Momentum Before = Angular Momentum After

Angular momentum is (rotational inertia)x(rotational velocity).  The two are inversely related.

Conservation of Momentum is best represented by ice skating.

As you can see in the diagram (found on ouchmath.wordpress.com), the speed of the speed, or the rotational velocity, is increased when the mass is closer to the axis of rotation.  This is represented by the formula below:

For the diagram on the left:

ROTATIONAL INERTIA x rotational velocity= Rotational Momentum

For the diagram on the right:
rotational inertia x ROTATIONAL VELOCITY=
Rotational Momentum

Note that the Rotational Momentum is the same in both equations, due to the Law of Conservation of Rotational/Angular Momentum.

CENTER OF GRAVITY AND TORQUES
Just as Ms. Lawrence said in the Course Video, all object have an average position of all of their mass.  This is called the Center of Gravity.  Your Center of Gravity essentially determines your balance.

The lower your center of gravity, the less likely you are to fall over.  To the left, we can see 3 trucks, with their Center of Gravities marked with an 'X'.  As long as their C of Gs are over their bases, the trucks will not fall over.  This means that trucks 'B' and 'C' will not fall over.

Another effecting factor of Center of Gravity is the width of the base.  The wider the base, the more likely that the C of G will be over the base, thus remaining balanced.  That is why many athletes are told to widen their stance, lowering their center of gravity and needing to be pushed further to fall down.


Torques cause rotation.  Torque = (f)x(lever arm).  Lever arms are the distance from the axis of rotation to the center of gravity.  Torques are best understood by the Lab that we did earlier in the unit.  For more information on this lab, check out my previous blog post, "Meter Stick Lab"

CENTRIPETAL FORCE


Centripetal force is a center-seeking force.  This is not to be confused with Centrifugal Force, which does not exist.  Centripetal forces is what keeps Race cars on inclined tracks, clothing in washing machines, and the airplanes in the sky.