Dinamica Dei Corpi Rigidi 1

The given statement is true. The unit "a" represents acceleration, and in this context, it refers to the angular acceleration. The unit of angular acceleration is measured in radians per second squared (rad/s^2). However, in this case, the unit is given as "radianti/s," which seems to be a typographical error. Therefore, the correct unit should be "radians per second" (rad/s), which represents the angular velocity. Thus, the given statement is true.

A rigid body refers to an object that does not deform or change shape while in motion. This means that the distances between its particles remain constant. Therefore, the statement "A rigid body retains its shape during motion" is true.

A rigid body is an object that does not deform under external forces. It can rotate around an axis and also translate or move in a straight line. Therefore, it is true that a rigid body can both rotate and translate.

A CD musicale dentro un lettore does not have a motion of translation. Instead, it spins or rotates within the CD player. Therefore, the statement is false.

The statement is true because according to the principle of conservation of angular momentum, the total angular momentum of a body or a system of particles remains constant if the resultant of the external torques acting on it is zero. This means that if there are no external torques acting on the body or system, its angular momentum will be conserved.

The moment of a force does depend on the origin and the point where the force is applied. The moment of a force is a measure of its tendency to cause rotation around a particular point or axis. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the point or axis of rotation. Therefore, the moment of a force is influenced by both the origin and the point where the force is applied.

The given statement is true. The SI unit of moment is Nm, which stands for Newton-meter. Moment is a physical quantity that measures the tendency of an object to rotate around a specific point or axis. The unit Nm represents the product of force (measured in Newtons) and distance (measured in meters), which is the basic formula for calculating moment. Therefore, the correct answer is true.

Every particle in a rigid body undergoes circular motion around the origin O.

The statement is true because angular velocity is defined as the rate at which an object rotates around a fixed axis. In a rigid body that is rotating, all points on the body are moving in circular paths around the same axis. Therefore, the angular velocity, which represents the speed of rotation, is the same for all points on the body.

In the comparison between linear and rotational dynamic quantities, force (F) corresponds to the moment of force (M). This means that when an object experiences a linear force, it also generates a rotational force or moment. Therefore, the statement that the force (F) corresponds to the moment of force (M) is true.

The motion of a kicked ball and the motion of a planet can be considered examples of rototranslation. The motion of a kicked ball involves both rotation (due to the spin imparted on the ball) and translation (as the ball moves through space). Similarly, the motion of a planet involves both rotation (as it spins on its axis) and translation (as it orbits around the sun). On the other hand, the motion of a suitcase on a conveyor belt and the motion of a sled do not involve rotation, only translation.

The correct answer states that in order to produce angular acceleration, a mechanical torque from the forces is required, and this torque is directly proportional to the moment of inertia. This is in accordance with the second law of dynamics for rotations around a fixed axis, which states that the torque applied to an object is equal to the moment of inertia multiplied by the angular acceleration. Therefore, the greater the moment of inertia, the greater the torque required to produce a given angular acceleration.

The statement "La velocità lineare è la stessa per tutti i punti del corpo rigido" translates to "The linear velocity is the same for all points of the rigid body." This statement is false. In a rigid body, different points can have different linear velocities depending on their distance from the axis of rotation. This is because the linear velocity of a point on a rigid body is directly proportional to its distance from the axis of rotation. Therefore, the linear velocity is not the same for all points of a rigid body.

The moment of inertia of a rotating rigid body depends on the axis of rotation, the geometric shape of the body, and the distribution of individual particles within the body. These factors determine how the mass is distributed and how it resists changes in its rotational motion. The axis of rotation determines the distance of each particle from the axis, affecting the moment of inertia. The shape of the body determines its mass distribution, which also affects the moment of inertia. The distribution of particles within the body determines how the mass is spread out, further influencing the moment of inertia. The rotational speed of the body does not directly affect the moment of inertia.

The given answer states that for an isolated system (not subjected to external forces), the following principles hold true: conservation of kinetic energy, conservation of momentum, conservation of angular momentum, and conservation of mechanical energy (for systems under conservative forces). These principles indicate that in an isolated system, the total amount of kinetic energy, momentum, angular momentum, and mechanical energy remains constant over time.

The correct answer is "ha un momento di inerzia pari a 1,60E-09 kg m m" and "ha un momento di inerzia pari a circa 0,000000002 kg m m". These answers state that the mass point has a moment of inertia equal to 1.60E-09 kg m m and approximately 0.000000002 kg m m, respectively. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution and the axis of rotation. In this case, the given mass point has a small moment of inertia due to its small mass and its distance from the axis of rotation.

The correct answer is "kg m m / s". This is the unit of measurement for angular momentum. It is derived from the product of mass (kg), distance (m), and velocity (m/s). The moment of inertia, which is the resistance of an object to changes in its rotational motion, is also involved in the calculation of angular momentum. Therefore, the unit of angular momentum is expressed as kg m^2/s.