A disk with a moment of inertia of 6915 kgm2 rotates at a sp

A disk with a moment of inertia of 69+1.5 kgm² rotates at a speed of of 143+5 radians/sec. Calculate the uncertainty in the kinetic energy. Include units.

Solution

I = Moment of inertia in percentage uncertainity = 69 +/- (1.5*100/69) = 69 +/- 2.17%

Omega = Rotation speed in percentage uncertianity = 143 +/- (5*100/143) = 143 +/- 3.50%

Kintetic energy = (0.5 x I x Omega²) = (0.5 x 69 x 143²) = 705490.5 Joule

Since KE is muliplicaiton of I and Omega raise to power two, these individual uncertailty shall add up in percentage to give total uncertainity of KE in percentage = 2.17 + 3.50 + 3.50 = 9.17%

So KE uncertianty = (9.17*705490.5)/100 = 64693.48 Joule