A wheel is rotating at a speed of 1000 rpm and its KE is `10^(6) J`. What is moment of inertia of the wheel about its axis of rotation ?

Explanation

Given, `v=1000 "rpm" =(1000)/(60)"rps"=(50)/(3)"rps"`
`omega=2piv=(100pi)/(3)"rads"^(-1)`
`because` Rotational kinetic energy `= (1)/(2)I omega^(2)`
`:. 10^(6)=(1)/(2)xxIxx((10pi)/(3))^(2)`
`rArrI=(2xx10^(5)xx9)/((100)^(2)pi^(2))=(200xx9)/(9.87)`
`=182.4 "kg-m"^(2)`.