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 many ...
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 arms ...
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, angular ...
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 the ...
Moment of Inertia
The comparability between linear and angular velocities, linear and angular accelerations, and the kinematic equations of translational and rotational ...
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 masses ...
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 multiplying ...
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 passing ...
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 the ...
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 through an ...
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 in a ...
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