A uniform brass disk of radius R and mass M with a moment of inertia I about its cylindrical axis of symmetry is at a temperature T = 45 °C. Determine the fractional change in its moment of inertia if it is heated to a temperature of 125 °C. (The linear expansion coefficient for brass is 1.90 10-5 °C−1.)
I tried finding the change in volume and using that ratio, but it isn't correct. Im not sure what the best approach is. Thank you for any suggestions!
3 answers
You have been given the linear expansion coefficient - find increase in radius R and then find the disk's MI.
ΔR=R•α•ΔT=R•1.9•10^-5•(125-45)=0.00152•R
R1=R+0.00152•R =R•1.001525
I=mR²/2
I1= mR1²/2= mR²•1.001525²/2=1.003• mR²/2=1.003•I
I1/I=1.003 or
I/I1=1/1.003=0.997
R1=R+0.00152•R =R•1.001525
I=mR²/2
I1= mR1²/2= mR²•1.001525²/2=1.003• mR²/2=1.003•I
I1/I=1.003 or
I/I1=1/1.003=0.997
thank you!
1 answer