A flywheel with a radius of 0.330 m starts from rest and accelerates with a cons

Question

A flywheel with a radius of 0.330 m starts from rest and accelerates with a constant angular acceleration of 0.580 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 .

Explanation / Answer

part a )

at the start t =0

flywheel starts from rest so w = wo = 0

atan = r *alpha = (0.330 ) * ( 0.580) = 0.1914 m/s^2

arad = rw^2 = 0

a = sqrt(atan^2 + arad^2) = 0.1914 m/s^2

part b )

atan = r*alpha = 0.1914 m/s^2

theta- thetao = 60 degree = 1.047 rad

wz^2 =w^2 + 2alpha*theta

wz = sqrt(2*alpha*1.047) = 1.102 rad/s

arad = r*w^2 = 0.40 rad/s^2

a = sqrt(arad^2 + atan^2)

a = 0.444 m/s^2

part c )

120 degree = 2.094 rad

wz = sqrt(2*0.580 * 2.094 ) = 1.5585 rad/s

arad = rw^2 = 0.80 rad/s^2

atan = r*alpha =0.1914 m/s^2

a = sqrt(arad^2 + atan^2)

a = 0.824 rad/s

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