Answer: angular acceleration = 0.748rad/s²
Explanation: according to the question, our answer needs to be in rad/s², thus all units in rev/s will be converted to rad/s
Assuming the motion of the object is of a constant angular acceleration, then newton's laws of motion is applicable.
The formulae below is used
v² = u² + 2αθ
v = final angular speed =6rev/s = 6*2π = 12π rad/s
u =initial angular speed =3.5rev/s = 3.5 *2π = 7π rad/s
Note 1 rev = 2π rad.
α = angular acceleration.
θ = angular displacement.
Diameter = 64cm = 0.64m, radius = 64/2 = 32cm = 0.32m
The angular displacement can be gotten using the formulae below
S = rθ, where s= linear distance covered = 200m, r = radius = 0.32m
θ = S/r = 200/0.32=625 rad.
By substituting the parameter we have that
(12π)² = (7π)² + 2α(625)
1421.22 = 486.31 + 1250α
1421.22 - 486.31 = 1250α
934.91 = 1250α
α = 934.91/1250
α= 0.748 rad/s²
