Torque

The work done by the applied force is converted into rotational kinetic energy of the disc. The torque acting on the disc is given by: Where: - is the force, - is the radius of the disc. The angular acceleration is given by: Where is the moment of inertia of the disc, and for a solid disc: Substituting values: Now, calculate the torque: Thus, the angular acceleration is: The angular velocity at the end of 2 seconds is: Thus, the angular velocity acquired by the disc at the end of 2 seconds is 16 rad/s.

The work done on the disc is: The work done on the disc is also equal to the change in rotational kinetic energy: For a solid disc, the moment of inertia is , so: Equating the work and kinetic energy: Solving for : Thus, the angular velocity acquired by the disc is .

The torque acting on the disc is given by: Where: - (force applied), - (radius of the disc). Thus: Now, the angular acceleration is given by the relation: Where is the moment of inertia of a solid disc: For this disc: - (mass of the disc), - (radius of the disc). So, the moment of inertia is: Now, the angular acceleration is: Finally, the angular velocity at the end of 2 seconds is given by: Substituting the values: Thus, the angular velocity acquired by the disc is 16 rad/s.