fertilizeki

2021-12-24

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 250 N applied to its edge causes the wheel to have an angular acceleration of 0.940 rad/s. What is the mass of the wheel?

Travis Hicks

Expert

The information below pertains to solid cylinder wheels rotating on a vertical axis without any friction.
$\alpha =0.94\frac{rad}{{s}^{2}}$

Torque is given by:
$\tau =F\cdot r=I\cdot \alpha$
Addressing the issue of moment of inertia
$I=\frac{F\cdot r}{\alpha }=\frac{250\cdot 0.33}{0.94}=87.8$
Inertia moment is determined by:
$I=\frac{1}{2}\cdot m\cdot {r}^{2}$
Solving it for mass:
$m=\frac{2\cdot I}{{r}^{2}}=\frac{2\cdot 87.8}{{0.33}^{2}}=1612.5$ kg

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