Problem 3 A flywheel has a radius of 0.67 m; however, because of its nonstandard

Question

Problem 3

A flywheel has a radius of 0.67 m; however, because of its            nonstandard geometry its moment of inertia about its center of          mass must be determined experimentally. In the experiment, a         block of mass = 11.8 kg is attached to a wire that is wrapped              around the flywheel such that no slipping can occur. The          flywheel/block system is released from rest (no initial velocity for          the block; no initial angular velocity for the flywheel), and the           block is observed to fall 3.00 m in 5.20 seconds.

Assuming that the effects of drag, friction, etc. are negligible, what           is the moment of inertia of the flywheel?

Problem 4

Problem 3 A flywheel has a radius of 0.67 m; however, because of its nonstandard geometry its moment of inertia about its centero mass must be determined experimentally. In the experiment, a block of mass-11.8 kg is attached to a wire that is wrapped around the flywheel such that no slipping can occur. The flywheel/block system is released from rest (no initial velocity for the block; no initial angular velocity for the flywheel), and the block is observed to fall 3.00 m in 5.20 seconds Assuming that the effects of drag, friction, etc. are negligible, what is the moment of inertia of the flywheel? Problem4 It is not necessarily realistic to assume that the effects of drag, friction, etc. are negligible in Problem 3. For example, there will always be a small amount of bearing friction between the axle of the flywheel and its supports unless special steps are taken to eliminate this (e.g., using magnetic fields to support the axle). One way to take this into account is to assume that there is always a small, constant torque applied to the axle of the flywheel that represents all of these "other" effects no matter what else is happening. The magnitude of this torque is not known and can only be determined by performing additional experiments. However, you may assume that this torque always acts to oppose (i.e., slow down) the rotation of the flywheel. To account for friction and other effects in this system, the flywheel from Problem 3 is subjected to a second test in which a block of mass 24.3 kg is attached and then the system is once again released from rest. In this experiment, it is observed that the block falls 3.00 m in 2.85 seconds. Using the results from this experiment and the experiment described in Problem 3, what is your new estimate for the moment of inertia of the flywheel?

Explanation / Answer

problem 3:

let linear acceleration be a m/s^2.

initial speed=u=0 m/s

distance fallen in t=5.2 seconds d=3 m

then using the formula:

distance=initial speed*time+0.5*acceleration*time^2

==>3=0*t+0.5*a*5.2^2

==>a=0.222 m/s^2

let tension in the rope be T N.

writing force balance equation for the mass:

m*g-T=m*a

==>T=m*(g-a)=113 N

angular acceleration=a/r=0.33118 rad/s^2

as torque=moment of inertia*angular acceleration

==>moment of inertia=torque/angular acceleration

=tension*radius/angular acceleration

=113*0.67/0.33118

=228.61 kg.m^2

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