Question

You need to design an industrial turntable that is 68.0 cm in diameter and has a kinetic energy of 0.290 J when turning at 35.0 rpm (rev/min).

Answer 1

Mass of the turntable = m

Diameter of the turntable = D = 68 cm = 0.68 m

Radius of the turntable = R = D/2 = 0.68/2 = 0.34 m

Moment of inertia of the turntable = I

The turntable is made in the shape of a solid disk therefore,

$I = \frac{mR^{2}}{2}$

Angular speed of the turntable = $\omega$ = 35 rpm = 35 x (2$\pi$/60) rad/s = 3.665 rad/s

Kinetic energy of the turntable = E = 0.29 J

Iw2 E 2

(mR²/2)w? E 2

$E = \frac{mR^{2}\omega ^{2}}{4}$

$m = \frac{4E}{R^{2}\omega ^{2}}$

$m = \frac{4(0.29)}{(0.34)^{2}(3.665)^{2}}$

m = 0.747 kg

Mass of the turntable = 0.747 kg