Kinetics of Rigid Body

Contents

**Define the following terms i. Mass and Weight ii. Momentum iii. Force of Inertia** 1

**Recall the following Laws: i. Law of Conservation of Momentum ii. Newton’s Law of Collision** 4

**Define Coefficient of Restitution** 5

**Define the following terms i. Mass and Weight ii. Momentum iii. Force of Inertia**

- Mass: Mass is a scalar quantity that measures the amount of matter present in an object. It is a measure of the object’s resistance to a change in its velocity, or its tendency to remain at rest or in uniform motion in a straight line. Mass is usually measured in kilograms (kg) or grams (g).
- Weight: Weight is a force that acts on an object due to the presence of gravity. It is the product of an object’s mass and the acceleration due to gravity. Weight is usually measured in Newtons (N) or pounds (lb).
- Momentum: Momentum is a vector quantity that measures the motion of an object. It is defined as the product of an object’s mass and velocity. Momentum is a measure of the object’s tendency to continue moving in the same direction at the same speed. The formula for momentum is given by p = mv, where m is the mass of the object and v is its velocity.
- Force of Inertia: Force of inertia, also known as the force of mass, is a force that resists a change in an object’s velocity. It is the product of an object’s mass and its acceleration. The formula for force of inertia is given by F = ma, where m is the mass of the object and a is its acceleration. This force arises from the fact that an object tends to resist any change in its velocity and will continue to move at a constant velocity unless acted upon by an external force.

**State the following Laws of Motion i. Newton’s 1st Law ii. Newton’s 2nd Law iii. D-Alembert’s principle iv. Newton’s 3rd Law**

- Newton’s 1st Law: Newton’s 1st Law, also known as the Law of Inertia, states that an object at rest tends to remain at rest, and an object in motion tends to remain in motion with a constant velocity, unless acted upon by an external force. This means that an object will not change its state of motion unless acted upon by a force. This law forms the basis of the concept of inertia and is closely related to the concept of mass.
- Newton’s 2nd Law: Newton’s 2nd Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for this law is given by F = ma, where F is the net force acting on the object, m is its mass, and a is its acceleration. This law states that for a given object, a larger force will result in a larger acceleration, and a smaller force will result in a smaller acceleration.
- D’Alembert’s principle: D’Alembert’s principle, also known as the principle of virtual work, states that the internal forces acting within a system are equal and opposite to the external forces acting on the system. This principle is used in the analysis of mechanical systems, such as machines and structures, to determine the forces acting on the system and their effects on the system’s motion.
- Newton’s 3rd Law: Newton’s 3rd Law, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This law states that the forces between two objects are always equal and opposite, meaning that if object A exerts a force on object B, then object B will exert an equal and opposite force back on object A. This law forms the basis of the concept of Newton’s third law, which states that forces always exist in pairs and are equal in magnitude but opposite in direction.

**Recall the following applications of Laws of Motion i. Motion of a Lift ii. Recoil of Gun iii. Motion of a Boat iv. Motion on Inclined Plane**

- Motion of a Lift: The motion of a lift is an application of Newton’s laws of motion. When a lift moves vertically, the forces acting on it include the gravitational force, the tension in the cable, and the normal force from the floor. Newton’s second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. The net force on the lift is used to determine its acceleration and its motion.
- Recoil of a Gun: The recoil of a gun is another application of Newton’s laws of motion. When a gun is fired, a force is exerted on the bullet, which then moves forward and a force is also exerted on the gun in the opposite direction. This is an example of Newton’s third law of motion, which states that for every action, there is an equal and opposite reaction. The recoil force on the gun is equal in magnitude but opposite in direction to the force exerted on the bullet.
- Motion of a Boat: The motion of a boat is an application of Newton’s laws of motion. The forces acting on a boat include the gravitational force, the buoyant force, and the drag force from the water. Newton’s second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. The net force on the boat is used to determine its acceleration and its motion.
- Motion on an Inclined Plane: The motion of an object on an inclined plane is an application of Newton’s laws of motion. When an object is on an inclined plane, the forces acting on it include the gravitational force, the normal force from the plane, and the frictional force. Newton’s second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. The net force on the object is used to determine its acceleration and its motion down the incline. The frictional force also plays a role in the motion, as it acts in opposition to the direction of motion and can affect the acceleration of the object.

**Define the term Collision**

A collision is a type of interaction between two or more objects that results in a change in their motion. A collision can be either elastic or inelastic, depending on the behavior of the objects involved.

In an elastic collision, the objects involved in the collision temporarily transfer energy between each other, but return to their original state after the collision. This means that the total kinetic energy of the system is conserved before and after the collision. An example of an elastic collision is the collision between two billiard balls on a pool table.

In an inelastic collision, the objects involved in the collision undergo permanent deformation, meaning that the total kinetic energy of the system is not conserved. In an inelastic collision, some of the energy is transformed into other forms, such as thermal energy or sound energy. An example of an inelastic collision is the collision between a car and a wall.

Collisions play an important role in many areas of physics, including mechanics, thermodynamics, and electromagnetic interactions. The study of collisions allows us to understand the behavior of objects in motion and the transfer of energy between objects, which is essential for many applications in fields such as engineering, transportation, and medicine.

**Recall the following Laws: i. Law of Conservation of Momentum ii. Newton’s Law of Collision**

- Law of Conservation of Momentum: The law of conservation of momentum states that the total momentum of a closed system is conserved, meaning that the total momentum before a collision is equal to the total momentum after the collision. This law is based on the principle of Newton’s third law of motion, which states that for every action, there is an equal and opposite reaction. In a collision, the momentum of one object is transferred to another object, but the total momentum of the system remains the same.

The law of conservation of momentum is a fundamental concept in physics and has many important applications, such as in the analysis of collisions, the motion of spacecraft, and the design of particle accelerators. It is a useful tool for understanding the behavior of objects in motion and predicting the outcome of collisions based on the initial conditions of the objects involved.

- Newton’s Law of Collision: Newton’s law of collision is a statement of the relationship between the forces acting on two objects during a collision and the resulting change in their motion. This law states that the time derivative of the relative velocity of two colliding objects is proportional to the force exerted by one object on the other.

Newton’s law of collision is a generalisation of the law of conservation of momentum and can be used to determine the velocity and motion of objects involved in a collision. The law of collision is an important tool for understanding the behavior of objects in motion, and it is widely used in fields such as engineering, sports, and medical physics to analyze and understand the behavior of objects in various types of collisions.

**Define Coefficient of Restitution**

The coefficient of restitution (COR) is a scalar value that represents the degree of elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of the two objects after the collision to the relative velocity of the two objects before the collision.

The coefficient of restitution ranges from 0 to 1. A value of 0 represents a perfectly inelastic collision, where the objects stick together after the collision and have zero relative velocity. A value of 1 represents a perfectly elastic collision, where the objects have the same relative velocity before and after the collision and conserve their total kinetic energy. Values between 0 and 1 represent partially elastic collisions, where the objects experience some degree of deformation but also conserve some of their kinetic energy.

The coefficient of restitution is an important parameter in the analysis of collisions, as it can be used to predict the behavior of objects in motion and the transfer of energy between objects. For example, it can be used to calculate the velocity and motion of objects involved in a collision, or to analyze the efficiency of energy transfer in a system. The coefficient of restitution is widely used in fields such as engineering, sports, and biomechanics to study the behavior of objects in motion and design systems that optimize the transfer of energy.

**Recall following Impacts of Collision i. Direct the collision of two bodies ii. Indirect the collision of two bodies**

- Direct Impact Collision: A direct impact collision is a type of collision in which two objects collide head-on, and the force of impact is applied directly to both objects. In a direct impact collision, the objects involved experience the maximum possible force of collision, as the relative velocity of the objects is highest. The force of the collision is proportional to the product of the mass and velocity of the objects involved, and it can cause significant deformation or destruction of the objects.

Examples of direct impact collisions include car crashes, football tackles, and hammer strikes. In these situations, the objects involved experience a high level of stress and deformation as a result of the direct impact.

- Indirect Impact Collision: An indirect impact collision is a type of collision in which two objects collide indirectly, such that the force of impact is not applied directly to both objects. In an indirect impact collision, the objects experience a lower force of collision than in a direct impact collision, as the relative velocity of the objects is lower. The force of the collision is proportional to the product of the mass and velocity of the objects involved, but it is distributed over a larger area.

Examples of indirect impact collisions include a ball bouncing off a wall, a billiard ball striking another billiard ball, and a baseball bouncing off a bat. In these situations, the objects involved experience a lower level of stress and deformation as a result of the indirect impact.