Question

A force of 30 N is applied tangentially to the rim of a solid disk of radius 0.10 m. The disk rotates about an axis through its center and perpendicular to its face with a constant angular acceleration of 150 rad/s^2. Determine the mass of the disk.

Answer 1

Answer:

m = 4.0 Kg

Explanation:

• Using an analogy with the Newton's 2nd law for point masses, for rigid bodies, the external net torque on a rigid body, is equal to its rotational inertia (I), times the angular acceleration (α) of the body, as follows:

       $\tau_{ext} = I* \alpha (1)$

• Since the magnitude of the torque is the product of the value of the force times the perpendicular distance between the line of action of  the force and the axis of rotation, and the force is tangential to the rim of the disk, we can write the following expression:

       $\tau = F*r*sin 90 = F*r (2)$    

• For a solid disk, the rotational inertia regarding an axis through its center, and perpendicular to its face is as follows:

      $I = \frac{m*r^{2}}{2} (3)$

• Replacing (3) in (1), and (2) in the left side of (1) also, we can solve for m, as follows:

       $m = \frac{2*30.0N}{0.1m*150(1/s2)} = 4.0 Kg (4)$

• So, the mass of the disk is 4.0 Kg.