Here we have to pause what weve learned about linear motion, and continue on with our circular motion discussion. Rotational kinematics describe the laws of motion of objects moving in a radial path and have unique terms such as angular velocity, to take the place of conventional linear components. As weve been saying, its important to know not only the math, but also the conditions of when to use such equations. Linear equations wont always work with radial problems, so its imperative that you pay attention to the problem at hand and first tell if its linear or radial.
Much like linear motion can be described by displacement, velocity, and acceleration, rotational motion can be described by angular (or rotational) displacement, angular velocity, and angular acceleration.
One complete revolution of a circular path describes 360 degrees, or 2 Pi radians, where a radian measures the distance around an arc equal to the length of the arc's radius.
Angular velocity describes the rate of change of an object's angular displacement. The right-hand rule describes the direction of the angular velocity vector, where counter-clockwise rotations correspond to positive angular velocities.
Angular acceleration describes the rate of change of an object's angular velocity. The right-hand rule also describes the direction of the angular acceleration vector.
Rotational analogs to the kinematic equations can be used to solve problems involving rotational motion.
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
I am Dan Fullerton and today we are talking about rotational kinematics.0003
Our objectives are going to be to understand the analogy between translational and rotational kinematics, to use the right-hand rule to associate angular velocity with a rotating object, and to apply equations of translational and rotational motion to solve a variety of problems.0008
Let us start by talking about radians and degrees.0027
In degrees, one time around a circle is 360 degrees.0029
In radians though, once around a circle is 2π, where a radian measures the distance around an arc equal to the length of an arc's radius.0034
So distance around a circle -- oftentimes written δS -- is the circumference, which is 2π radians or it would be 360 degrees if you are looking at an angular measurement.0043
A clown rides a unicycle. If the unicycle wheel begins at rest and accelerates uniformly in a counterclockwise direction to an angular velocity of 15 rpms in a time of 6 s, find the angular acceleration of the unicycle wheel.0378
Let us start by converting this 15 rpms to radiants per second. We have 15 rpms or revolutions per minute. 0393
We need minutes to go away, so I will put minutes on the top and I want seconds here, so I know 1 minute is 60 seconds and now I have revolutions per second (rps).0403
So, I also need to multiply to make the revolutions go away.0413
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