Question

Establish the relation-V= ωr, where V= Linear speed, (ω)=angular speed, r= radius of the circular path

Answer 1

Linear velocity=displacement÷time

angular velocity ,w= angular displacement÷time

so here time =angular displacement÷angular velocity

substituting this in first equation.

linear velocity=displacement÷(angular displacement÷angular velocity)
=displacement×angular velocity ÷(angular displacement)

On a full rotation in a circle , its moves a distance equal to circumference. So
displacement or distance here taken =2πr

angular displacement=360°=2π
for a rotation

so V= 2πr × w ÷(2π)
=rw....

so proved.