Question

A wheel of diameter 50.0 cm starts from rest and rotates with a constant angular acceleration of 2.00 rad/s^2. At the instant the wheel has computed its second revolution, compute the radial acceleration of a point on the rim in two ways.
(1)Using the relationship .
arad=w2r
(2)from the relationship
arad=v2/r

Answer 1

R = 25 cm = 0.25 m
α = 2.00 rad /s²
T(heta) = 4 π
ω = T(heta)/ t
ω = α t
α t = 4 π / t
t ² = 2 π
t = √ ( 2π )  = 2.5 s
ω = α t = 2 · 2.5 = 5 rad/s
v = ω r = 5 · 0.25 = 1.25 m/s
(1)    a (rad) = ω² r = 25 · 0.25 = 6.25 m/s²
(2)    a (rad) = v² / r = ( 1.25 )² / 0.25 = 0.15625 / 0.25 = 6.25 m/s²