The flywheel (a massive disk or ring used for storing energy as rotational kinet
ID: 1966997 • Letter: T
Question
The flywheel (a massive disk or ring used for storing energy as rotational kinetic energy) of an oldfashioned steam engine was running at constant angular speed, but then at t = 0 the steam was shut off, and friction due to the bearings and the air gradually bring it to rest. During the spin-down, the angular velocity was observed to be (t) = 39.3s-1-(1.98*10-4s-3)t2 .
a) What was the initial, constant angular speed in revolutions per minute?
b) After how many minutes does the wheel come to rest?
c) How many rotations does the wheel make before coming to rest?
d) What is the tangential linear acceleration of a point that is 50 cm from the axis of rotation at t = 440 seconds ?
e) What is the total linear acceleration of that point at that time?
Explanation / Answer
a) At t=0, = 39.3 rad/s =(39.3/2)*60 = 3703.9 or 3704 revolutions/minute
b) =0; 0 = 39.3 - 0.000198t2 => t = 445.51 seconds => t = 7.425 minutes
c) Angular acceleration = d/dt = -2*0.000198*440 = -0.17424
Linear acceleration at the given point = -0.50*0.17424 = -0.08712 m/s2
d) Centripetal acceleration at that point = r*2 = 0.5*0.935 = 0.4677 m/s2
Therefore, total linear acceleration = (0.087122+0.46772) = 0.4757 m/s2