Determine the kinetic energy of a circular disc rotating with a speed of 60 rpm about an axis passing through a point on its circumference and perpendicular to its plane. The circular disc has a mass of 5 kg and radius 1 m.

Explanation

Mass of disc, M = 5kg, Radius R = 1m ltbgt Angular velocity `omega = 60 RPM = (60xx2pi)/(60) = 2pi` Rad/sec.
M.O.I of disc about a point passing through circumference and perpendicular to the plane
`I' = I_(G) + MR^2` ltbtgt But `I_(G) = (MR^2)/(2)` (for above case)
`therefore I' = (MR^2)/(2) + MR^2 = 3/2 MR^2`
Rotational kinetic energy ` = 1/2 Iomega^2`
` = 1/2 . 3/2 MR^2 xx (2pi)^2`
`therefore R.K.E. = 3/4 xx 5 xx 1 xx 1 xx 2 xx 3.142 xx 2 xx 3.142`
` =15 xx 3.142 xx 3.142 = 148.1 `