A flywheel with a radius of 0.230m starts from rest and accelerates with a const

Question

A flywheel with a radius of 0.230m starts from rest and accelerates with a constant angular acceleration of 0.690rad/s2.

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?. Find atan and arad in m/s2

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?. Find atan and arad in m/s2

Explanation / Answer

atan = r * alpha = 0.230 * 0.690 = 0.1587 m/s2

theta = 60 degrees = 60 * 2 * pi / 360 = 1.047 radians

w1 = 0, theta = 1.047 radians

w22 - w12 = 2 * alpha * theta

w2 = sqrt (2 * alpha * theta)

w2 = 1.20 rad/s

arad = r * w22 = 0.230 * 1.202

arad = 0.33 m/s2

atan = 0.1587 m/s2

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B) theta = 120 degrees = 120 * 2 * pi/360 = 2.094 radians

w1 = 0, theta = 2.094 rad

w22 - w12 = 2 * alpha * theta

w2 = sqrt (2 * alpha * theta)

w2 = 1.699 rad/s

arad = r * w22 = 0.230 * 1.6992

arad = 0.66 m/s2

atan = 0.1587 m/s2

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