The flywheel of a motorhas a mass of 35 kg and a moment ofinertia of 58 kg . m2. The motor develops aconstant torque of 250 N . m, and the wheel starts fromrest. A. What is the angular acceleration of the flywheel? B. What is its angular velocity as it makes 450revolutions? C. How much time is needed to achieve the first 450revolutions? The flywheel of a motorhas a mass of 35 kg and a moment ofinertia of 58 kg . m2. The motor develops aconstant torque of 250 N . m, and the wheel starts fromrest. A. What is the angular acceleration of the flywheel? B. What is its angular velocity as it makes 450revolutions? C. How much time is needed to achieve the first 450revolutions?
Explanation / Answer
A) Use the equation = I. Solvingfor (the angular acceleration) gives: = /I = (250 N m)/(58 kgm2) = 4.3 rad/s2 B) Use the kinematics equation for rotational motionf2 = o2 +2. Note that since it starts at rest,o = 0. f = sqrt(o2 +2) = sqrt(2) = sqrt(2(4.3rad/s2)(450 rev)(2 rad/rev)) = 160 rad/s C) Use the kinematics equation for rotational motion t =(f - o)/. t = ((160 rad/s) - (0 rad/s))/(4.3 rad/s2) =36s B) Use the kinematics equation for rotational motionf2 = o2 +2. Note that since it starts at rest,o = 0. f = sqrt(o2 +2) = sqrt(2) = sqrt(2(4.3rad/s2)(450 rev)(2 rad/rev)) = 160 rad/s C) Use the kinematics equation for rotational motion t =(f - o)/. t = ((160 rad/s) - (0 rad/s))/(4.3 rad/s2) =36s