Glossary
Topic 4 Foundation Engineering “A”
Peter,
Yes it’s glossary time again……………..
Angular Displacement:
In the case of rotary (angular) motion, angular displacement (rad) is the angle,
measured in radians, swept out by an object as it circles around some point – this
point being the centre of the circle. The rotation may either be clockwise or
anticlockwise, so that angular displacement will have a sign.
Angular Velocity:
Angular velocity (rad s-1) is the rate of change of angular displacement. The
angular velocity may be positive or negative depending on direction of rotation.
Angular Acceleration:
Angular acceleration (rad s-2) is the rate of change of angular velocity. The
angular acceleration may be positive or negative depending on direction of
rotation and whether angular velocity is increasing or decreasing.
Radian:
Angles at the centre of a circle may be expressed either in degrees or radians.
Any angle at the centre of a circle, radius “r”, will subtend an arc of length “s” at its
circumference. The angle in radians is the ratio of “s” divided by “r”. Radians in SI
units are written as (rad). It is a dimensionless quantity being a distance divided
by a distance – when cancelling units it may be struck out, because it has no
dimensions.
Sign Convention:
Angular displacement and velocity are positive in an anticlockwise direction and
negative in a clockwise direction. For angular acceleration the sign may be
positive or negative in either direction depending on whether angular velocity is
increasing or decreasing.
Periodic Time:
Periodic time (s) is the time taken to sweep out one complete revolution of a
circle. The periodic time has no sign associated with its value.
Angular Kinematic Relations:
These expressions provide all the relationships between angular displacement “θ”,
angular velocity (initial “ωo” and final “ω”), angular acceleration “α” and time “t”
needed to solve angular motion problems – the assumption underlying their
derivation is one of constant angular acceleration, which results in a linear angular
velocity time relationship. Thus, simple arithmetic average angular velocities may
be used. They are the angular analogues of the linear kinematic relations.
Tangential Speed:
Tangential speed is the linear speed (m s-1) that an object has at any distance
from the centre of the circle around which it is circling. At constant angular velocity
the tangential speed is directly proportional to the distance – that is, the distance
from the point of interest to the centre of the circle.