A torque of 12 N.m is applied to a solid , uniform disk of radius 0.50 m. If the disk accelerates at 5.7 rad/s^2 , what is the mass of the disk?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A torque of 12 N*m is applied to a solid, uniform disk of radius 0.50 m. As a result of this, the disk accelerates at 5.7 rad/s^2.

If a torque T is applied to an object with moment of inertia I, the result angular acceleration is a, where T = I*a

Here, T = 12 N*m, a = 5.7 rad/s^2

`I = T/a = 12/5.7`

The moment of inertia of a uniform solid disk of mass m and radius r, being rotated about a perpendicular line through the center, is equal to `(1/2)*m*r^2`

Here `12/5.7 = (1/2)*m*0.5^2`

=> `m = (12/5.7)*(2/0.5^2)`

=> m `~~` 16.84 kg

The mass of the disk is approximately 16.84 kg

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