Question

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

Answer 1

Answer:

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

Explanation:

Let θ be angular displacement

θ = (2π)* no of relolutions = 2π * 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

Hope it helps :)

Answer 2

Answer:

Angular velocity (w) = 2 п/3 rad/s,

Linear speed (v) = 2 /3 m/s,

Centripetal acceleration (a) = (2 п/3)^2 m/s^2

Explanation:

Let Φ be angular displacement

Φ= (2T)* no of relolutions = 2π * 20 = 40π

w = 8/t

[t= time]

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

=>w= 40/60= 2/3 rad/s

w 2π/3 rad/s

v=rw

..v=2n/3 m/s

a= (v^2)/r

= (2 π/3)^2/1

a= (2 п/3)^2 m/s^2

Hope it helped you ☞ ☆