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The kinematics of rotational motion describes the relationships between the angle of rotation, angular velocity, angular acceleration, and time. It only describes motion—it does not include any forces or masses that may affect rotation (these are part of dynamics).
Observe the kinematics of rotational motion. Derive rotational kinematic equations. Evaluate problem solving strategies for rotational kinematics. Just by using our intuition, we can begin to see how rotational quantities like θ, ω and α are related to one another.
Learning Objectives. By the end of this section, you will be able to: Understand the relationship between force, mass and acceleration. Study the turning effect of force. Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.
The rotor equations of motion may be expressed in terms of the Cartesian coordinates of the elastic axis (X, Y) or by using the polar coordinates Z and O. At zero speed, the point C lies along the origin of the coordinates. The complex amplitude Z is Z = X + i Y = Complex Rotor Displacement with amplitude A and phase angle Orelative to the x axis
Rotational kinematics is the study of how rotating objects move. Let’s start by looking at various points on a rotating disk, such as a compact disc in a CD player. EXPLORATION 10.1 - A rotating disk. Step 1 – Mark a few points on a rotating disk and look at their instantaneous velocities as the disk rotates.
The formula v = r is true for a wheel spinning about a fixed axis, where v is speed of points on rim. A similar formulas v CM = r works for a wheel rolling on the ground. Two very different situations, different v’s: v = speed of rim vs. v cm = speed of axis. But v = r true for both.
Make graphs of angular speed vs. radius (i.e. string length) and linear speed vs. radius. Describe what each graph looks like. If you swing an object slowly, it may rotate at less than one revolution per second.
