Question

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/s2. What is the mass of the wheel?

Answer 1

Answer:

The mass of the solid cylinder is $m = 1612.5 \ kg$

Explanation:

From the question we are told that

   The radius of the grinding wheel is $R = 0.330 \ m$

   The  tangential force is $F_t = 250 \ N$

    The angular acceleration is  $\alpha = 0.940 \ rad/s^2$

The torque experienced by the wheel is mathematically represented as

     $\tau = I * \alpha$

Where  I  is the moment of inertia

The torque experienced by the wheel can also be  mathematically represented as

       $\tau = F_t * r$

substituting values

       $\tau = 250 * 0.330$

      $\tau = 82.5 \ N\cdot m$

So

   $82.5 = I * \alpha$

    $82.5 = I * 0.940$

So

   $I = 87.8 \ kg \cdot m^2$

This moment of inertia can be mathematically evaluated as

     $I = \frac{1}{2} * m* r^2$

substituting values

  $87.8 = \frac{1}{2} * m* (0.330)^2$

=>   $m = 1612.5 \ kg$