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In a uniform circular motion,

omega = w = angular velocity = angle in radians per unit time

r = radius of circle the body is moving in

Ф = angle made by moving body

dФ/dt =

d

d

= 2

directed radially inwards

d

**= linear tangential speed (or velocity) - constant speed***v*omega = w = angular velocity = angle in radians per unit time

**linear acceleration = dv/dt***a =*r = radius of circle the body is moving in

Ф = angle made by moving body

dФ/dt =

**, So r***w***= r dФ/dt = d***w***/dt =***s***(s is the arc length traveled in dt time)***v***= r***v**w*d

**/dt = acceleration =***v**a*d

**= Vector difference between velocity at t =t+dt and t = t***v*= 2

**cos (π/2 - dФ/2) = 2***v***sin dФ/2 = (approximately)***v***dФ***v*directed radially inwards

d

**/dt =***v***dФ/dt =***v***w***v**So a = v w = r w² = v²/r directed radially inwards*