A solid cylindrical disk has a radius of 0.15 m. It is mounted to an axle that is perpendicular

step 1 So for this problem, we need the formula that the net torque is equal to the moment of inertia t

A solid cylindrical disk has a radius of 0.15 m. It is...

A solid cylindrical disk has a radius of $0.15 \mathrm{m}$. It is mounted to an axle that is perpendicular to the circular end of the disk at its center. When a $45-N$ force is applied tangentially to the disk, perpendicular to the radius, the disk acquires an angular acceleration of $120 \mathrm{rad} / \mathrm{s}^{2} .$ What is the mass of the disk?

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Key Concepts

Newton’s Second Law for Rotation

Newton’s second law for rotation states that the net torque acting on an object is equal to the product of its moment of inertia and its angular acceleration. This principle is fundamental in relating the applied forces to the resulting rotational motion.

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the lever arm (the perpendicular distance from the axis of rotation to the line of action of the force). It is the rotational equivalent of linear force and determines how effectively a force will produce rotational acceleration.

Moment of Inertia

The moment of inertia quantifies an object’s resistance to changes in its rotational motion about a specific axis. It depends on both the mass of the object and its distribution relative to the axis of rotation. For common shapes, standard formulas exist that simplify the calculation of the moment of inertia.

Angular Acceleration

Angular acceleration is the rate at which an object’s rotational speed changes over time. It is analogous to linear acceleration in translational motion and is directly linked to the net torque applied to the object, as expressed in the rotational form of Newton’s second law.

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