Question

a stone is tied to one end of a string and is whirled in a horizontal circle of radius 1m at 20 rpm . calculate the angular velocity and linear speed of the stone find the centripetal acceleration​

Answer 1

The value of centripetal acceleration is a = (2 π/3)^2 m/s^2

We know that:

• Angular velocity ( ω) = 2 π/3 rad/s
• Linear speed (v) = 2 π/3 m/s
• Centripetal acceleration (a) = (2 π/3)^2  m/s^2

Solution:

Let Theta (θ) be angular displacement

θ = (2π)  x no of revolutions = 2π x 20 = 40π

ω = θ / t                  [t= time]

Here 20 revolutions in 1 min => 40π radians swept in 60 s

=> ω = 40π/60 =  2π/3  rad/s

∴ ω =  2π/3  rad/s

v = rω       [r=radius = 1m]

∴v = 2π/3 m/s

a = (v^2)/r

=  (2 π/3)^2 /1

∴a = (2 π/3)^2 m/s^2

#SPJ2