Question

A boy is running along a Circular track of 15 m diameter. If in 20 seconds he covers half the track, then find his Angular speed and Linear speed?

Answer 1

The angular speed of the body is calculated as ω = θ/t

Here θ = 180 degrees =1 radians. (since the boy has completed half the circular track)
    or 1 radian = 57.296 degrees.
t = 20 seconds.

So ω = θ/t
      ω = 1802018020,
      ω = 9 degree/s
      ω = 0.157 radians/s.

Now to find his Linear speed, we need to convert the radians in meters and then using the relation of
Linear and angular speed we can find the Linear speed of the boy.
V = r ω
   = 152152 meters ×0.157 radians/s.
V = 1.1775 m/s.
So, the Linear speed of the boy is 1.1775 m/s.