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Angular motion angular kinematics

Outline. TorqueAngle-angle diagramsInertiaAngular displacementAngular speed and velocityLinear velocity of a point on a rotating bodyAngular acceleration. The relationship of torque, rotational inertia, and angular acceleration. The relationship of angular acceleration, net torque, and the s

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Angular motion angular kinematics

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    1. Angular motion (angular kinematics) A torque is a measure of the capacity of force acting at a point to cause rotation about an axis. Torques occur for external and internal forces. The external force causes the body to rotate about an axis, but internal forces can occur in equal and opposite pairs so that the sum of their moments about a point vanishes in a state of equilibrium. If internal forces are not in equilibrium then motion ensues.

    2. Outline Torque Angle-angle diagrams Inertia Angular displacement Angular speed and velocity Linear velocity of a point on a rotating body Angular acceleration

    3. The relationship of torque, rotational inertia, and angular acceleration The relationship of angular acceleration, net torque, and the system’s mass characteristics is similar to that expressed for linear acceleration, net force and mass.

    4. Newton’s first law of motion in its angular form A rotating body will continue to turn about its axis of rotation with constant angular momentum unless an external couple or eccentric force is exerted upon it. This law is also known as the principle of conservation of angular momentum.

    5. Newton’s second law of motion in angular form The angular acceleration of a body is directly proportional to the net torque applied to it, and the body’s acceleration is inversely proportional to the rotational inertia of the body.

    6. Newton’s second law of motion in angular form This can be expressed mathematically as: Angular acceleration = torque rotational inertia ? = T I The body’s mass is the inertial resistance to linear motion or linear acceleration. However mass is only one component of rotational inertia (or moment of inertia), the resistance to change for rotary motion also depends on the distribution of the mass from the point axis of rotation.

    7. The angular form of Newton’s third law For every torque that is exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first.

    8. Angular motion Angular motion occurs when all parts of a body move through the same angle but do not undergo the same linear displacement. Angular motion occurs about an axis of rotation that is a line perpendicular to the plane motion in which the rotation occurs.

    9. A wheel as an example of rotational motion

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