Problem 2. A flywheel with a radius of 0.25 m starts from rest and accelerates w

Question

Problem 2. A flywheel with a radius of 0.25 m starts from rest and accelerates with a constant angular acceleration of 1.00 rad/s? about a horizontal axis through its center. (a) Compute the magnitudes of the radial (or centripetal) acceleration, the tangential acceleration, and the total acceleration for a point on its rim 1 sec after the flywheel begins rotating (b) What is the angle between the total acceleration and the radial acceleration? (c) What is the angular mo mentum about the fly heel about the aos of rotation at t#2.0 seconds?

Explanation / Answer

2(a) w = w0 + alpah t = 0 + (1 x 1) = 1 rad/s

a_r = w^2 r = 0.25 m/s^2 ....Radial acc.

tangential, a_t = alpha r = 0.25 m/s^2

total acc., a = sqrt(a_t^2 + a_r^2) = 0.35 m/s^2

(b) theta = tan^-1(a_t/a_r) = 45 deg

(c) w = 0 + (2 x 1) = 2 rad/s
angular momentum = I w

= (m 0.25^2) (2)

= 0.125 m

put the mass m in kg and angular momentum will be in kg m^2 / s .

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