Rotational and Tangential Velocity
-Tangential velocity is the velocity of something moving along a circular path. The direction of motion is tangent to the circumference of the circle. Another word for tangential speed is linear speed. Tangential speed depends on the radial distance ( distance from the axis).
-Rotational velocity involves the number of rotations or revolutions around an axis per unit time. Rotational velocity is often measured in RPM (rotations per minute). Rotational speed will be the same at any distance from the axis of rotation.
An excellent situation in which to observe rotational and tangential velocity is on a merry go round. All of these children are traveling at the same rotational velocity, because they are making the same number of revolutions in a given time. However, the kids on the outer edge of the merry go round are moving at a faster tangential velocity than the kids towards the center of the merry go round. This is because they are covering a much larger distance in the same amount of time that the kids toward the inside are covering a very small distance.
Rotational Inertia
Rotational inertia is the property of an object to resist changes in spinning. It depends on mass and its distribution. When the mass is closer to the axis of rotation it has less rotational inertia, so it speeds up, and when it is farther from the axis, it has more rotational inertia, so it slows down. So why does velocity change?
Conservation of Angular Momentum
We've learned about the conservation of momentum, ptotalbefore = ptotalafter; p = mv; mvbefore = mvafter. This same same rule applies to rotational or angular momentum. In this case, rotational speed is velocity is conserved, so angular momentum before = angular momentum after. Angular momentum is based on two things: rotational inertia and rotational velocity, so angular momentum = rotational inertia x rotational velocity; rotational inertia x rotational velocity = rotational inertia x rotational velocity.
In this video, we can see how the ice skater's angular momentum is conserved when she lessens her rotational inertia by bringing her arms in and increases her rotational velocity:
http://www.youtube.com/watch?v=AQLtcEAG9v0
Torque
Torque causes rotation. It is equal to force x lever arm. A lever arm is the distance from the axis of rotation. There are three things that affect torque: changing the force, changing the lever arm, or both. Torque is measured in Nm (Newton meters). The more torque an object has, the easier it is to rotate.
My group made a podcast about torque that further explains it implications:
http://www.youtube.com/watch?v=fOPdbmeks4A
Center of Mass/Gravity
All objects have an average position of their mass, called their center of mass. When gravity acts on that center of mass, it is called center of gravity. Center of gravity affects balance. When an object's center of gravity is inside of its base of support, it is less likely to fall over than when it center of gravity is outside of its base of support. When center of gravity is outside of the base of support, a lever arm is created, and the force of gravity gives the object torque, causing it to fall over.
This is exemplified in the following image:
The object with the smaller base of support will fall over because its center of gravity is outside of its base of support, while the large one will remain standing.
Centripetal/Centrifugal Force
Centripetal force is a center-seeking force that keeps objects going into a curve when rotating. Centrifugal force is a fictitious, fleeing force that causes an object to feel as if it is being flung outward.
One example of centripetal force is a satellite orbiting earth. One might ask, how does a satellite not end up being flung out of orbit or crashing into earth? Satellites are able to stay in earth's orbit, because they have the perfect velocity, so they don't cancel out the centripetal force (gravity) acting on them.
Below is a satellite orbiting the earth and a diagram of the forces and velocity.
Satellites orbit, because they have the force of gravity pulling them towards earth, but how do things like airplanes turning have a centripetal force? Their centripetal force is a resultant of Flift and Fweight.
This is also exemplified in car on a banked race track. The resulting centripetal force keeps the car on the racetrack.
What I have found difficult about what I have studied is accepting that centrifugal force does not exist, but we feel something and call it centrifugal force and study it. I overcame these difficulties by listening carefully to class discussions and realizing that centrifugal force is a feeling, not an actual force.
My problem-solving skills, effort, and learning…
In this unit, I have completed all of my homework in a timely manner and participated in class. My group members and I created a helpful podcast about torque, and we worked well together. I found that I improved my blog posts, because I found a useful drawing app and learned how to properly link my video sources.
My goals for the next unit are to continue completing my work on time and improve my blog posts by providing more visual explanations and thorough descriptions.
