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Chapter 4: Problem 18

Statement-1 : In a frame of reference attached to a particle itself, the acceleration of the particle is zero. Statement-2: The frame of reference which moves with constant velocity w.r.t. another frame of reference is an inertial frame of reference.

Short Answer

Expert verified
In its own frame, a particle has zero acceleration, aligning with inertial movement as described in Statement-2.

Step by step solution

01

Analyze Statement-1

Statement-1 posits that in a frame of reference attached to the particle itself, the acceleration of the particle is zero. This statement is consistent with the basic definition of acceleration, as any particle viewed in its own rest frame would not appear to change its velocity and hence would have zero acceleration.
02

Analyze Statement-2

Statement-2 states that a frame of reference which moves with constant velocity relative to another frame is an inertial frame. This is the definition of an inertial frame, where no external forces (other than uniform motion) act on the frame.
03

Compare the Two Statements

We now compare the conclusions from both statements. Statement-1 describes a condition of zero acceleration when viewing a particle in its own frame, while Statement-2 describes the behavior of frames with respect to relative uniform motion. These concepts are related because if a particle is in an inertial frame, relative motion does not affect the observation of zero acceleration in the particle鈥檚 own frame.
04

Concluding Observations

Statement-1 is a specific case of observation (i.e., particle's self frame), while Statement-2 is a principle of motion between frames. Statement-1 can be derived from the condition of an inertial frame as described in Statement-2. However, the zero acceleration in Statement-1 is due to the viewpoint, not because of inertia alone.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Inertial Frame
An inertial frame of reference is crucial to understanding physics. It is essentially a perspective or viewpoint where the laws of motion operate normally without any external, non-uniform forces acting.
This means that any object in an inertial frame moves with a constant velocity unless acted upon by an external force.
In other words, if you are observing a particle from an inertial frame, the particle should not accelerate unless a force is applied.
  • Inertial frames are fundamental to Newton's first law of motion, which states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by a net external force.
  • These frames are often used as reference points to simplify and understand the complex interactions in different physical systems.
  • In real life, most frames are non-inertial because they experience acceleration due to forces such as gravity. Therefore, inertial frames are often idealized in theoretical studies.
The Nature of Acceleration
Acceleration is a key concept that describes how the velocity of an object changes over time. In its simplest form, acceleration occurs when there is a change in speed or direction.
For example, when a car speeds up, slows down, or turns, it is accelerating.
Mathematically, acceleration can be expressed as \( a = \frac{\Delta v}{\Delta t} \), where \( a \) represents acceleration, \( \Delta v \) is the change in velocity, and \( \Delta t \) is the change in time.
  • A positive acceleration means the object is speeding up, while a negative acceleration (often called deceleration) means the object is slowing down.
  • It's important to note that even a change in the direction of motion equates to acceleration because velocity is a vector quantity, encompassing both magnitude and direction.
  • In an inertial frame following a particle with constant velocity, the observed acceleration is zero, which aligns with the idea proposed in the first statement.
Exploring the Rest Frame
A rest frame is a specific type of inertial frame where the object being observed appears to be at rest. This means the object has zero velocity relative to this frame.
In a rest frame, any object appears to have no movement, thus the perceived acceleration is zero.
This aligns with Statement-1, as in the rest frame of a particle, its acceleration appears to be zero.
  • The rest frame is useful for simplifying the analysis of motion, especially when examining objects in a system only relative to each other.
  • It serves as a basis for understanding other reference frames, helping to determine how the motion of an object varies between different perspectives.
  • Switching between rest frames can offer insights into the nature of relative motion and how different observers perceive the same event.
  • Just like with any frame, external forces acting upon objects may change their rest state, making it a dynamic point of reference in practical applications.

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Most popular questions from this chapter

When forces \(\vec{F}_{1}, \vec{F}_{2}, \vec{F}_{3} \ldots \vec{F}_{n}\) act on a parlicle, the particle remains in cquilibrium. If \(\vec{F}_{1}\) is now removed then acecleration of the particle is (a) \(\frac{\vec{F}_{1}}{m}\) (b) \(-\frac{\vec{F}_{1}}{m}\) (c) \(\frac{\vec{F}_{2}\left|\vec{F}_{3}\right| \ldots \mid \bar{F}_{n} \vec{F}_{1}}{m}\) (d) \(\frac{\overline{F_{2}}}{m}\)

A block of mass \(10 \mathrm{~kg}\) is placed in a car going down an incline of inclination \(60^{\circ}\). If the coefficient of friction between the block and car floor is \(\frac{1}{\sqrt{3}}\). Find the acceleration \(a\) of car down the incline so that the block doesn't slip on the car surface. (a) \(a \geq \frac{g}{\sqrt{3}}\) (b) \(\alpha \geq \frac{2 g}{\sqrt{3}}\) (c) \(a<\frac{g}{\sqrt{3}}\) or \(a>\frac{2 g}{\sqrt{3}}\) (d) \(\frac{g}{\sqrt{3}} \leq a \leq \frac{2 g}{\sqrt{3}}\)

If a body is placed on an inclined plane, the forces acting on the body are (a) gravitational (b) electromagnetic (c) nuclear (d) weak

A block of mass \(m\) connceted with a fixed point by a light inextensible string is kept on a smooth wedge of mass \(M\) and angle of inclination \(\theta\). If the string is parallel to the inclinc at the time of its release, find the (a) lension in the string, (b) accelerations of \(M\) and \(m\), (c) contact forces belween \(M\) and \(m\), (d) reaction force oflered by ground on the wedge.

A water pipe has an intemal diameter of \(10 \mathrm{~cm}\). Water flows through it at the rate of \(20 \mathrm{~m} / \mathrm{sec}\). The water jet strikes normally on a wall and falls dead Find the forec on the wall. Solution Mass of water flowing through the tube per second \(=A v \rho\) where \(A=\) area of cross section and \(v=\) velocity of water of density \(\rho\). Momentun change/second \(=A v \rho v=A v^{2} \rho\) Thus, the forec on the wall \(=A v^{2} \rho=\pi \times\left(\frac{5}{100}\right)^{2} \times(20)^{2} \times 1000=3143 \mathrm{~N}\)
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