Angular Motion of the System

Differences between linear and angular kinematics

1. Eccentric force is applied, and therefore torque is present. 2. There is a specified axis of rotation. 3. A segment rotating around an axis may have the ability to travel completely in a circle. Therefore, the number of revolutions may be specified.

Angular acceleration

A change in magnitude and/or direction of the angular velocity vector with respect to time

Momentum

A system's quantity of motion **In angular momentum situations, possessing large amounts of momentum means that large torque must be applied to stop rotation.

Centripetal acceleration

Acceleration caused by change in direction of the velocity vector

What force would cause linear acceleration of an object?

Applying a centric force causes linear acceleration of an object.

Instantaneous angular acceleration

Change in angular velocity at one specific instant in time.

Average angular acceleration

Change in angular velocity divided by the entire interval over which it changed.

What results from changes in the radius of rotation or changes in angular velocity?

Changes in angular momentum are normally the result of changes in the radius of rotation (which changes the moment of inertia) or changes in angular velocity Changes in angular momentum are directly related to Newton's first two laws of motion.

Angular position

Distance (radius) from the origin, and the angle between the chosen reference axis and the line formed by connecting the given point to the origin.

What force causes angular acceleration of an object?

Eccentric forces cause angular acceleration of an object

Newtons 3rd law

For every torque, there is a torque of equal magnitude directed in the opposite direction

Newton's 1st law

If an object is at rest it will not undergo angular displacement without the application of an external eccentric force (torque). Without angular displacement, angular velocity is equal to zero. If the object is already rotating with a given velocity, there will be no change in that angular velocity without an externally applied eccentric force. If there is not change in angular velocity, then there is no angular acceleration of the system.

What is the most efficient way to move the human body?

In most situations, the most efficient way to move the human body is to maximize acceleration while minimizing torque requirements

Tangential linear acceleration

Linear acceleration of a point of a rotating segment.

What type of force is required for angular motion to occur?

The applied force must be eccentric

Torque

Torque is applied to the implement by the person The implement exerts a torque of equal magnitude to the person The person and implement share a common axis of rotation Both objects are affected by a common torque

Principle moment of inertia

When referring to the moment of inertia with respect to one of the principle axes of rotation

Angular displacement

change in angular position of a segment or any point on the rotating segment Measured in degrees or radians

Displacement

change in position

Velocity

change in position relative to the interval in which it takes place

Acceleration

change in velocity relative to the interval in which the change takes place observed change in motion

Kinetic energy

energy associated with motion.

Absolute angular position

if the reference axis cannot move

Relative angular position

if the reference axis is capable of moving

Angular impulse

interval of torque application

Tangential linear velocity

linear velocity of a point on a rotating segment *The linear velocity vector of the point on the segment is tangent to the path of the object and perpendicular to the radius of the circular path.

Peak rate of motion

max rate of motion achieved

Work

product of applied force and the magnitude of displacement in the direction of applied force.

Instantaneous speed and instantaneous velocity

rate of motion at one given instant in time

Rotational kinetic energy

rotational inertia and its angular velocity.

Angular speed

scalar rate of angular motion

Rotational power

the amount of angular mechanical work performed during a given interval.

Power

the amount of mechanical work performed in a given interval

Rotational work

the angular displacement of an object about an axis caused by the application of a torque

Rotational inertia

the resistance of an object to having its state of angular motion changed. Mass and mass distribution are factors.

Angular velocity

the vector rate of angular motion