A flywheel with a radius of 0.310 m starts from rest and accelerates with a cons

Question

A flywheel with a radius of 0.310m starts from rest and accelerates with a constant angular acceleration of 0.660rad/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. 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?.

Please explain all steps clearly.

Explanation / Answer

A) a_tan = r*alfa = 0.31*0.66 = 0.2046 m/s^2

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


w1 = 0, theta = 1.047 radians

w2^2 -w1^2 = 2*alfa*theta

w2 = sqrt(2*alfa*theta)

w2 = 1.1754 rad/s

a_rad = r*w2^2 = 0.4283 m/s^2
a_tan = 0.2046 m/s^2


a_total = sqrt(a_tan^2 + a_rad^2)

a_total = 0.4747 m/s^2

C)
theta = 120 degrees = 60*2*pi/360 = 2.094 radians


w1 = 0, theta = 2.094 radians

w2^2 -w1^2 = 2*alfa*theta

w2 = sqrt(2*alfa*theta)

w2 = 1.6623 rad/s

a_rad = r*w2^2 = 0.8566 m/s^2
a_tan = 0.2046 m/s^2


a_total = sqrt(a_tan^2 + a_rad^2)

a_total = 0.88 m/s^2

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