Question

formula of angular speed

Answer 1

Angular speed is the rate at which an object changes its angle (measured) in radians, in a given time period. Angular speed has a magnitude (a value) only.

Angular speed = (final angle) - (initial angle) / time = change in position/time

ω = θ /t

ω = angular speed in radians/sec

θ = angle in radians (2π radians = 360 degrees)

t = time, sec

Angular speed and angular velocity use the same formula; the difference between the two is that Angular speed is a scalar quantity, while angular velocity is a vector quantity.

Angular Speed Formula Questions:

1) The earth rotates once on its axis every 24 hours. What is its angular speed?

Answer: The angle traversed, 1 rotation, means that θ = 2π. The time for this rotation, t = 24 hr. Time must be converted to seconds.

t = 24 hr x 60 min/hr x 60 sec/min = 86400 sec

ω = θ /t

ω = 2π/86400 sec

ω = 0.0000726 radians/sec = 7.26 x 10-5 rad/sec

Answer 2

Heya..........!!!

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• Derivation. :-»

Let :

( v ) => Linear Velocity .

( ω ) => Angular Velocity .

There is a realtion between linear displacement and angular displacement .

let angular displacement be ( x )

Angle which is moved by particle (  θ )

radius ( r )

=>  θ = x / r
=> x = r θ .............( i )

in this equation ( i ) divide both side by ( t ) time

=> x / t = rθ/t

=> x / t. = v ,,  θ/t. = ω

v = rω




$\large\boxed{\omega = v/r}$






Hope It Helps You. ☺