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Torque is an essential concept in physics, particularly when dealing with rotational motion. It is the rotational equivalent of linear force and measures how much force is acting on an object to make it rotate. Torque is calculated using the formula:- \( \tau = F \times r \)- \( F \) is the force applied- \( r \) is the perpendicular distance from the pivot point (axis of rotation) to the line of action of the forceIn the context of the problem, when a force of 45 N is applied tangentially to the disk, torque helps us determine the twisting force responsible for the motion. It is important to ensure that the force is applied correctly (perpendicular to the radius) to maximize the produced torque.

Angular acceleration is all about the rate of change of angular velocity over time. It tells us how quickly a rotating object speeds up or slows down its spin. Consider the equation:- \( \tau = I \times \alpha \)- \( \tau \) is torque- \( I \) is the moment of inertia- \( \alpha \) is angular accelerationThis equation shows that angular acceleration is directly proportional to torque and inversely proportional to the moment of inertia. In simple terms, the greater the torque applied to an object, the more quickly it accelerates unless it has a large moment of inertia. For our problem, the given angular acceleration of 120 rad/s² helps us calculate the moment of inertia and, subsequently, the mass of the disk.

Moment of inertia quantifies how difficult it is to change the rotational motion of an object. It's similar to mass in linear motion, but for rotation. Every object has a unique moment of inertia based on its shape and distribution of mass. For a solid cylinder rotating about its central axis, such as our disk, the moment of inertia is:- \( I = \frac{1}{2} m r^2 \)- \( m \) is the mass of the object- \( r \) is the radiusUnderstanding the moment of inertia is crucial when you need to find how mass influences rotational movement. In the exercise, calculating this helps us ultimately determine the mass of the disk.

A solid cylinder is a common shape in physics problems, especially those involving rotation. This shape, thanks to its symmetrical nature around its axis, makes it straightforward to calculate various physical quantities like torque, angular acceleration, and moment of inertia. Key characteristics of a solid cylinder include: - Uniform mass distribution - Revolves around its central axis When calculating the properties of a solid cylinder, remember the formulas associated with its geometry and consider the axis about which it rotates. These calculations allow us to determine quantities such as moment of inertia and leverage other properties to find the mass, as the problem required.