Q9P The angular momentum of a partic... [FREE SOLUTION]

Chapter 6: Q9P (page 289)

The angular momentum of a particle m is defined by $L = mr 脳 (\frac{dr}{dt})$ (see end of Section 3). Show that $\frac{dL}{dt} = mr 脳 \frac{d^{2} r}{{dt}^{2}}$

Short Answer

Expert verified

The proof is given as follows.

\frac{dL}{dt} = mr 脳 \frac{d^{2} r}{{dt}^{2}}

Step by step solution

Given equation

The angular momentum of a particle m is defined by $L = mr 脳 (\frac{dr}{dt})$ .

Definition of Angular Momentum

The angular momentum L of m about point O is defined by the equation $L = r 脳 (mv) = mr 脳 v$

Proof of the statement

To prove the given condition, Consider,

$L = mr 脳 (\frac{d^{2} r}{{dt}^{2}})$ ,then:

$\frac{dL}{dt} = m \frac{dr}{dt} 脳 \frac{dr}{dt} + mr 脳 \frac{d^{2} r}{{dt}^{2}}$

But since the cross product of a vector with itself results in the zero vector, then:

$\frac{dL}{dt} = mr \frac{d^{2} r}{{dt}^{2}}$

Hence, the result is $\frac{dL}{dt} = m \frac{dr}{dt} 脳 \frac{dr}{dt} + mr 脳 \frac{d^{2} r}{{dt}^{2}}$

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91影视

The angular momentum of a particle m is defined by $L = mr 脳 (\frac{dr}{dt})$ (see end of Section 3). Show that $\frac{dL}{dt} = mr 脳 \frac{d^{2} r}{{dt}^{2}}$

Short Answer

Step by step solution

Given equation

Definition of Angular Momentum

Proof of the statement

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91影视

The angular momentum of a particle m is defined by L=mr脳(drdt)(see end of Section 3). Show thatdLdt=mr脳d2rdt2

Short Answer

Step by step solution

Given equation

Definition of Angular Momentum

Proof of the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Translational Dynamics

Magnetism

Electricity and Magnetism

Quantum Physics

Nuclear Physics

Study anywhere. Anytime. Across all devices.

The angular momentum of a particle m is defined by $L = mr 脳 (\frac{dr}{dt})$ (see end of Section 3). Show that $\frac{dL}{dt} = mr 脳 \frac{d^{2} r}{{dt}^{2}}$