Chapter 10
Rotation and Rigid Bodies
Uniform circular motion is motion in a circle at a constant speed. Although this is the simplest case of rotational motion, it is very useful for…
We previously discussed angular velocity for uniform circular motion, however not all motion is uniform. Envision an ice skater spinning with their…
If angular acceleration is constant, then we can simplify equations of rotational kinematics, similar to the equations of linear kinematics. This…
Kinematics is the description of motion. The kinematics of rotational motion discusses the relationships between rotation angle, angular velocity,…
If the rotational definitions are compared with the definitions of linear kinematic variables from motion along a straight line and motion in two and…
In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by…
The comparability between linear and angular velocities, linear and angular accelerations, and the kinematic equations of translational and…
The rotational kinetic energy of a body is equal to half the square of its angular speed and the moment of inertia.
This relationship between the…
The moment of inertia of an object depends on its axis of rotation. Consider a barbell consisting of two masses attached to the ends of a rod. The…
The moment of inertia is a quantitative measure of the rotational inertia of an object. It is defined as the sum of the products obtained by…
The parallel-axis theorem provides a convenient and quick method of finding the moment of inertia of an object about an axis parallel to the axis…
The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of…
Consider a vector rotating about an axis with an angular velocity, such that its tip sweeps a circular path.
In time Δt, the vector moves…
An accelerating particle experiences a force equal to the mass multiplied by the acceleration in an inertial frame of reference. Consider a particle…
Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System
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The possibility to generate and measure rotation and torque at the nanoscale is of fundamental interest to the study and application of biological…
Classical techniques for investigating the Rayleigh-Taylor instability include using compressed gasses1, rocketry2 or linear electric motors3 to…
Experimental Procedure for Warm Spinning of Cast Aluminum Components
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High performance, cast aluminum automotive wheels are increasingly being incrementally formed via flow forming/metal spinning at elevated…
