Center of Mass
The center of mass of an object is the average position of its mass and the center of gravity is the specific point upon which gravity acts. These two points are not always the same. The center of mass and center of gravity are pertinent to the topic of rotation because their location can affect how easily an object can rotate.
Whether or not an object will fall over or not can be determined by the location of its center of gravity over its base of support. If the center of gravity falls inside of an object's base of support, it is stable. However, if the center of gravity falls outside of the base of support, the object is unstable.
For example, look at these images of the leaning Tower of Pisa.
The base of support of an object is its base. For the leaning Tower of Pisa, the base of support is the circumference of the bottom of the tower. However, for people, our base of support is based (pun semi-intended) on how wide apart we have our feet planted. The wider our base of support, the harder it is to push us over. This is why coaches often tell players to stand with their legs bent, shoulder width apart. The reason we bend our legs is because the closer our center of gravity is to our base of support, the farther we will have to rotate to get the center our center of gravity outside of our base of support.
At the end of this video by some classmates, this concept is illustrated by some members of the wrestling team.
Rotational and Tangential Velocity
Tangential speed is the same linear speed we've talked about in past units. In terms of circular motion, tangential speed is the linear speed of something moving along a circular path. The direction of the linear motion is tangent to the circumference of the circle. Just like usual, this is measured in meters per second (m/s) or kilometers per hour (km/h).
Rotational speed is the speed at which an object rotates over an amount of time. This is measure in rotations per minute (rpm).
Watch this video of kids on a merry go round, if the girl in the orange shirt and the boy in the striped shirt have the same rotational velocity, what does this mean about their tangential velocities?
The girl in the orange shirt has a faster tangential velocity than the boy in the striped shirt because she must cover a farther linear distance than he does in the same amount of time.
Conversely, gears in a system work by having the same tangential velocity and a different rotational velocity. This can be observed in the video below:
Torque
Torque is what causes rotation. It is calculated using the formula force x lever arm. Lever arm can be defined as the distance between the axis of rotation and where the force is applied. It is perpendicular to the force. If a large rotation occurs, it is because there is a large torque. Large torque can be caused by a large force, a large lever arm or both.
When an object is balanced, there are two torques: clockwise and counter-clockwise. The two are equidistant from the center of gravity.
An example of how torque affects daily life is when you try to open a door with a push handle. If you push on the door closer to the hinges, the axis of rotation, you need more force to open the door because the lever arm is small. However, pushing at the opposite end of the door makes it easy to open because of the distance between where your hands are pushing on the door and the hinges--thus giving you a larger torque.
This video gives a good explanation of torque and calculations.
Rotational Inertia
Rotational inertia is the property of an object to resist changes in spin. Since we know that with inertia more mass means more inertia, we also know that the distribution of mass is important when it comes to what makes an object inclined to spin or remain still. A great example of distribution of mass and rotational inertia is in figure skating when the skaters tuck in their arms to spin faster. Watch as this skater's speed increases when she tucks her arms and legs in.
Conservation of Angular Momentum
This is a concept that goes hand in hand with rotational inertia and is similar to concepts we've discussed in the past. Just like the conservation of linear momentum, this means that momentum before = momentum after. Angular momentum is calculated by multiplying rotational inertia x rotational velocity.
Angular momentum before = angular momentum after.
RI x RV before = RI x RV after.
Let's put this in terms of the video we just watched. Before she tucks in her arms and legs her rotational inertia is very large, but her rotational velocity is much smaller. Therefore, to conserve her angular momentum after she tucks in her arms and legs, her rotational inertia must be very small and her rotational velocity must be much larger.
That looks like this:
RI x RV = RI x RV
If you're still having trouble with the concept, this video has a quick explanation and lots of good (and easy to re-create!) demonstrations.
Centripetal Force
Centripetal force is the force that makes an object curve. Centripetal force is the reason you stay inside of a roller coaster that goes in loop-di-loops and the reason clothes stay inside a top-loading washing machine during the spin cycle.
Here's an explanation of why water leaves the barrel of a washing machine, but clothes stay in:
Centripetal force is the center-seeking force hat causes an object to curve. The water droplets are acted upon by the centripetal force and the water droplets are not being acted upon by any force. They just continue to move straight forward, straight through the holes, which we know happens because of the property of inertia.
Centrifugal force does not exist and is not the reason that you hit the car door when you round corners or why the water droplets come out of the basin. Those simply happen because as a person/object in motion without an outside for acting upon you/it forward motion continues until an outside force is met.
These are some cool experiment done to show centripetal force.
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