Angular velocity : The rate of change of angular displacement with time is called the angular velocity (co) of the particle.
the angular displacements of the particle in time t and t + bt are 9 and 9 + 59 respectively.
Therefore the average angular velocity of the particle in time 51 is given by
angular displacement average angular velocity = --
The limiting value of this ratio when 8 t tends to zero gives the instantaneous angular velocity 0) at time t.
Angularvelocity can also be defined as the angle traced per unit time by the radius vector. The SI unit of angular Velocity is radians per second (rad/s).
Understanding Units of Acceleration is always challenging for me but thanks to all math help websites to help me out.
Angularvelocity is a vector quantity and like instantaneous angular displacement (50), it can be represented in magnitude and direction by using the right hand rule. In vector notation, dQ
» = - ...(1.5)
Angular acceleration : If the angular velocity of a particle moving along a circle is not constant but goes on changing, the particle has angular acceleration (a). For example, when we switch on an electric fan, the angular velocity of each particle of its blades initially goes on increasing. In this case, the fan has angular acceleration.
Angular acceleration is defined as the rate of change of angular velocity. If the angular velocity changes from OJj to <u2 in time t,
change in angular velocity
average angular acceleration =-^r^-
aav = -JLy± -(1.6)
If the angular velocity changes from co to co + 8 co in a short time interval 8t, instantaneous angular acceleration is given by
„ _ lim Sm da
The SI unit of angular acceleration is rad/s2. Like angular velocity, angular acceleration is a vector quantity. In vector form,
« = f ...(1.8)
Angularacceleration can be represented in magnitude and direction by using the right hand rule. If the angular velocity is increasing, the direction of angular acceleration (a) is the same as that of cb. However, if angular velocity is decreasing, the direction of a is
opposite to that of (0.
Ifa particle moving along a circle is subjected to a linear accelerationin the tangential direction, its linear speed (v) does not remain constant. The magnigude (a) of the tangential linear acceleration is given by
dv d 5®
a= It ^Jt=(m) = r St
( du\ a = r a '••« = — ...(1.9)
I dt )
:. tangential linear acceleration = radius x angular acceleration