Question

# A flywheel with a radius of .340 m starts from rest and accelerates with a constant...

A flywheel with a radius of .340 m starts from rest and accelerates with a constant angular acceleration of .730 rad/ s2.
A) compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start.
B) compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0.
C) compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 120

ar=r*ω^2

at =r*α

r= 0.34 m ,ω is the angular velocity, α = .730 rad/s2

A)

at =r*α = 0.34*0.730 = 0.2482 m/s2

ar=r*ω^2 = 0.34*0 = 0 m/s2

resustant = sqrt(at ^2 +ar ^2) =   0.2482 m/s2

B)​

at =r*α = 0.34*0.730 = 0.2482 m/s2

θ = 60 deg = 60 *π/ 180 = π/3

ωf^2 = ωi^2 + 2*α*θ​

ωf = sqrt (2*α*θ​) = sqrt( 2*.730*π/3) = 1.23649037 rad/s^2

ar = 0.34*1.23649037^2 =0.519828868 m/s2

resultant acceleration = sqrt( 0.2482^2 +0.519828868^2) =0.576042787 m/s2

C)

same ways

at =r*α = 0.34*0.730 = 0.2482 m/s2

θ = 120 deg =120 *π/ 180 = 2π/3

ωf^2 = ωi^2 + 2*α*θ​

ωf = sqrt (2*α*θ​) = sqrt( 2*.730*2π/3) = 1.74866145 rad/s^2

ar = 0.34*1.74866145^2 =1.03965773 m/s2

resultant acceleration = sqrt( 0.2482^2 +1.03965773^2) =1.06887391 m/s2

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