socorraob

2021-12-31

A 250 g , 25-cm diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1900 rpm in 4.7 s ? Express your answer in newton-meters.

Jonathan Burroughs

Expert

Mass of the disc, m = 250 g = 0.25 kg
Diameter of the disc, d = 25 cm = 0.25 m
Disc rotate from 0 to 1900 rmp, in t = 4.7 sec.
Moment of inertia of the disc
$I=\frac{1}{2}m{\gamma }^{2}=\frac{1}{2}\left(0.25\right){\left(\frac{0.25}{2}\right)}^{2}$

angular frequency, $\omega =2\pi \left(\frac{1900}{60}\right)$

$\omega =\alpha$

The torque is
$\tau =I\alpha =\left(0.00195\right)\left(42.33\right)$

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