A solid cylindrical disk has a radius of 0.17 m. It is mounted to an axle that is perpendicular to the circular end of the disk at its center. When a 35-N force is applied tangentially to the disk, perpendicular to the radius, the disk acquires an angular acceleration of 100 rad/s2. What is the mass of the disk?
To determine the mass of the disk, we can use the equation:
Torque = Moment of Inertia * Angular Acceleration
The torque applied to the disk can be calculated using the formula:
Torque = Force * Radius
Substituting the given values:
Torque = 35 N * 0.17 m
To find the Moment of Inertia, we need to consider the shape of the disk. The Moment of Inertia for a solid cylinder rotating about its center axis (perpendicular to the circular face) can be calculated using the formula:
Moment of Inertia = (1/2) * Mass * Radius^2
Since we are trying to find the mass, let's rearrange the formula:
Mass = (2 * Moment of Inertia) / Radius^2
Substituting the known values:
Mass = (2 * Torque) / (Angular Acceleration * Radius^2)
Now we can substitute the values into the equation:
Mass = (2 * (35 N * 0.17 m)) / (100 rad/s^2 * (0.17 m)^2)
Simplifying the equation:
Mass = (2 * 5.95 Nm) / (0.100 Ns^2)
Mass = 2 * 59.5 kg
Mass = 119 kg
Therefore, the mass of the disk is 119 kg.