Dynamics Class 12 Mathematics Notes has been updated according to the latest syllabus of 2080. It means the notes of dynamics chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.
Chapter – 19
Dynamics
In Class 12 mathematics, the chapter on dynamics is focused on understanding the motion of objects and the forces that influence this motion. It involves using calculus, particularly differentiation and integration, to analyze how particles move under various forces.
This chapter also delves into relative motion, examining how the motion of objects is perceived in different frames of reference, particularly in terms of velocity and acceleration.
Dynamics Class 12 Mathematics Notes PDF
This PDF will provide the solutions of every question from the 2nd exercise of class 12 dynamics chapter. If you want the notes of other exercises then you can choose from the button given above.
Please repost this PDF on any website or social platform without permission.
Definition of force
In physical sciences, it has now become a common practice to accept the term ‘Force’ as one of the undefinables (i.e. primitive term) and use it to define other concepts. We, however, for practical purpose give a workable definition of force on the basis of Newton’s first law of motion.
As explained earlier, the property of inertia of a body has no tendency of its own to change its state of rest or uniform motion. If it is not acted upon by some external force, it will remain either at rest or in uniform motion. That is, its original or natural state remains undisturbed or unbroken. A force is always necessary to cause any change in the state or uniform motion of a body. This is why we may define a force in the following way:
A force is that which acting on a body.changes or tends to change the state of rest or of uniform motion of the body. The fact that inertial property of a body lies at the foundation of physical sciences, gave rise to the new name ‘Principle of inertia’ or ‘Law of inertia’ to Newton’s first law of motion
Mass and Momentum
The definition of force derived from Newton’s first law of motion tells us that a force acting on a given body affects its property of inertia. Attempts to describe by how much or how little a given force acting on a given body changes its inertia, gave rise to one of the fundamental notions of physical sciences, namely, the notion of ‘Mass’ of the body, usually denoted by italic m. We now proceed to do this.
To measure or describe by how much or how little a given force acting on a given body hanges its amount of inertia content, we may assign to each body a numerical quantity (or factor or multiplier) that describes how much or how little it changes its state of rest or uniform motion per unit time (i.e. it accelerates) under the action of a given force. This quantity is called the ‘mass’ of the body, and is denoted by the symbol m (italic).
Suppose a given force act on two bodies of masses m1 and m2 the accelerations of the two bodies are also different. Experiments of various types show that a body of smaller mass acquires a greater acceleration as compared with a body of larger mass. If a1 and a2 are the accelerations of two bodies of masses m1 and m2 under the action of the same force, the ratio a2/a1 may be used to compare the two masses.
For definitions, the convention used is to say that the larger mass, m1 say, is a2/a1 times the mass m2 and write m1 = (a2/a1) × m2.
This equation may be used to measure the mass of a given body by comparison with a standard unit of mass. A standard unit of mass is called the kilogramme kg. It is the mass of a solid cylinder made of platinum-iridium alloy kept at the International Bureau of Weights and Measures at Sivres, near Paris.
Given two bodies with masses m, and m₂, the mass of the composite body formed by fastening them together can be measured as described above. It is actually found to be m₁ + m2 at all times. Thus, mass is found to be additive and is directly related to the quantity of matter. This explains the use of the term ‘mass’ by Newton to mean ‘quantity of matter’.
If the solutions PDF of dynamics chapter was helpful to you then feel free to leave your comments sharing your thought and opinions. You can also join our telegram channel to remain connected with us. We keep on posting all the latest news and notes in our telegram group. So we’ll be happy if you be a part of it.
