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# Chapter 10 Rotation and Rigid Bodies

## Angular Velocity and Displacement

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…

## Angular Velocity and Acceleration

We previously discussed angular velocity for uniform circular motion, however not all motion is uniform. Envision an ice skater spinning with their…

## Rotation with Constant Angular Acceleration - I

If angular acceleration is constant, then we can simplify equations of rotational kinematics, similar to the equations of linear kinematics. This…

## Rotation with Constant Angular Acceleration - II

Kinematics is the description of motion. The kinematics of rotational motion discusses the relationships between rotation angle, angular velocity,…

## Relating Angular And Linear Quantities - I

If the rotational definitions are compared with the definitions of linear kinematic variables from motion along a straight line and motion in two and…

## Relating Angular And Linear Quantities - II

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…

## Moment of Inertia

The comparability between linear and angular velocities, linear and angular accelerations, and the kinematic equations of translational and…

## Moment of Inertia and Rotational Kinetic Energy

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…

## Moment of Inertia: Calculations

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…

## Moment of Inertia of Compound Objects

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…

## Parallel-axis Theorem

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…

## Perpendicular-Axis Theorem

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…

## Vector Transformation in Rotating Coordinate Systems

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…

## Coriolis Force

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…

## Magnetically Induced Rotating Rayleigh-Taylor Instability

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…

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