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Tangential velocity is the velocity, or speed in a given direction, of an object traveling in a circle multiplied by the radius of that circle. Velocity is similar to speed, but it takes into account the direction the object is moving, whereas speed does not. This type of velocity involves continual circular motion, making it quite different from linear velocity, which measures objects traveling in a straight line.
Angular velocity is this term for how fast a wheel is spinning. This speed is multiplied by the radius of the wheel to yield the tangential velocity. It increases as the distance from the center of the circle increases.
A tangent is a line that touches a curve. When a wheel is resting on a road, for example, the straight line of the road touching the wheel is tangent to the curve of that wheel. In tangential velocity, the tangent must be the same direction as the spin of the wheel.
The radius is a linear measurement from the center of a circle to its the outer edge. The diameter of a circle is the distance across a circle, so the radius is exactly half the diameter. Since tangential velocity increases as radius increases, it is greater on a larger wheel, even if it's spinning at the same speed as a smaller wheel.
Speed is the distance an object travels divided by time. In circular motion, the distance traveled is the circumference of the wheel, which is measured in revolutions per second, or how many times the circle goes around in one second. Interestingly, the speed and forces on a spinning wheel vary at different points on that wheel.
The children’s playground ride known as a merry-go-round can offer a concrete example for understanding the abstract topic of tangential velocity. When riding in the center of the merry-go-round, the ride does not seem to travel very fast, and it may be easy to hang on. On the outer edge of the merry-go-round, however, the ride seems to spin so fast that children cling with all their might to keep from flying off. In actuality, the outer edge must cover a greater distance in the same spin as points closer to the center, so it has greater velocity — in other words, it is going faster on the outside than in the middle.
I feel stupid because I can't visualize how the outer point could move faster (although logically it makes total sense), if the wheel moves at one speed and the points extending outward remain aligned.