A uniform disc of mass 100 g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along a horizontal table with a velocity of 20 cm `s^(-1)`. (take the surface of table as reference).

Explanation

Mass of the disc m = 100 g = 0.1 kg.
Diameter of the disc d = 10 cm
Radius of the disc r = 5 cm = 0.05 m
Rolling with a velocity v = 20 cm `s^(-1) = 0.20 ms^(-1)`
Total energy of the disc `E_(Tot) = ?`
`E_(Tot)` = Translational K.E. + rotational K.E.
Moment of inertia (M.I) of the disc about its own axis,
`I = (1)/(2) mr^(2) , v = r omega because omega^(2) = (v^(2))/(r^(2))`
Rotational K.E. `= (1)/(2) I omega^(2) = (1)/(2) xx ((1)/(2)mr^(2)) xx ((v^(2))/(r^(2)))`
`=(1)/(4) mv^(2)`
T.E `= (1)/(2) mv^(2) + (1)/(4) mv^(2) = (3)/(4) mv^(2)`
T.E. of the disc `E_(Tot) = (3)/(4) xx 0.1 xx 0.20 xx 0.20`
= 0.003 J.