Pulley 1. A flywheel has its mass distributed non-uniformly and has an unknown m

Question

Pulley 1. A flywheel has its mass distributed non-uniformly and has an unknown moment of inertia. Its mass radius is o20 metersand is mounted on a vertical rotational axis. A string of negligible mass is wrapped around the rim of the wheel; passes over a small, lightweight, frictionless pulley as shown. When a student applies a constant downward force of 5 N on the string, the flywheel rotates at a constant angular speed. The student stops the flywheel and re-wraps the string. She then applies a 20 N force to the string. Starting from rest, the wheel's angular speed now increases linearly over time. A computer records the velocity of a point on the rim of the flywheel as a function of time, as shown below 1.75 1.50 1.25 1.00 0.75 0.50 0.25 Corstauto 025 0.30 03540 045 050 055 Time ( (a) Caleulate the moment of inertia of the disk from the data and the given information. of 0,925.-0,29 3,85

Explanation / Answer

We know

Slope of v vs t gives acceleration a

Assuming graph as straight line

a=(1.46-0.76)/(0.5-0.3)=3.5 m/s^2

Let tension in the rope be T

T=20N

T*0.2=I*3.5/0.2

Putting the value

We got

I=0.228 kgm^2

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