![]() ![]() When it comes to translational motion, we tend to talk about position in terms of x and y. So the rules here are the same, but rotational motion has what you might call its own circular logic. Like when a point on a spinning wheel is actually standing still. It still involves things like position, velocity, and acceleration, and many of the equations we used to describe rotational motion will look really familiar to you, but there are some important differences, like instead of positions, there are angles. Instead of points along a line, you follow points along an arc, and there are times when rotational motion can explain things that sound impossible, but are actually true. ![]() But the physics of rotational motion isn't all that different from the physics of translational motion. But rotational motion is also a thing, and an important one.įor example, the spin of a football, both the soccer and the non-soccer kind, will affect the way it flies through the air. Kinematics is concerned with the description of motion without regard to force or mass.At this point, we've covered a lot of the basics when it comes to how things move, but we've mostly been focusing on only one type of motion: translational motion, which is when something moves through space, but doesn't rotate. Kinematics for rotational motion is completely analogous to translational kinematics, first presented in One-Dimensional Kinematics. It is also precisely analogous in form to its translational counterpart. This last equation is a kinematic relationship among \(\omega, \alpha\), and \(t\) - that is, it describes their relationship without reference to forces or masses that may affect rotation. The radius \(r\) cancels in the equation, yielding \ where \(\omega_o\) is the initial angular velocity. Now, let us substitute \(v = r\omega\) and \(a = r\alpha\) into the linear equation above: As in linear kinematics, we assume \(a\) is constant, which means that angular acceleration \(\alpha\) is also a constant, because \(a = r\alpha\). To determine this equation, we recall a familiar kinematic equation for translational, or straight-line, motion: \ Note that in rotational motion \(a = a_t\), and we shall use the symbol \(a\) for tangential or linear acceleration from now on. Let us start by finding an equation relating \(\omega, \alpha\), and \(t\). The kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time. The wheel’s rotational motion is exactly analogous to the fact that the motorcycle’s large translational acceleration produces a large final velocity, and the distance traveled will also be large.Kinematics is the description of motion. In more technical terms, if the wheel’s angular acceleration \(\alpha\) is large for a long period of time \(t\) then the final angular velocity \(\omega\) and angle of rotation \(\theta\) are large. For example, if a motorcycle wheel has a large angular acceleration for a fairly long time, it ends up spinning rapidly and rotates through many revolutions. Just by using our intuition, we can begin to see how rotational quantities like \(\theta, \omega\) and \(\alpha\) are related to one another. ![]() Evaluate problem solving strategies for rotational kinematics.Observe the kinematics of rotational motion.\)īy the end of this section, you will be able to: ![]()
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