A flywheel with a radius of 0.250m starts from rest and accelerates with a const

Question

A flywheel with a radius of 0.250m starts from rest and accelerates with a constant angular acceleration of 0.800rad/s2 .

Part A

Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start.

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Part 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?.

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Part 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?.

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Explanation / Answer

A.

a_tan = alpha .r = 0.8 x 0.25 =0.2 rad/s2

a_rad = 0 ( initial angularvel. is zero)

a_total = 0

B. )

a_tan = alpha .r = 0.8 x 0.25 =0.2 m/s2

w^2 -0 = 2 x 0.8 x (60 x pi / 180)

w = 1.29 rad/sec

a_rad = w^2.r = 1.29^2 x 0.250 = 0.42 m/s2

a_total = sqrt(a_tan^2 + a_rad^2) = 0.464 m/s2

C)

a_tan = alpha .r = 0.8 x 0.25 =0.2 m/s2

w^2 -0 = 2 x 0.8 x (120 x pi / 180)

w = 1.83 rad/sec

a_rad = w^2.r = 1.83^2 x 0.250 = 0.84 m/s2

a_total = sqrt(a_tan^2 + a_rad^2) = 0.86 m/s2

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