Chapter 13.4, Problem 44E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

If a particle with mass *m* moves with position vector **r**(*t*), then its **angular momentum** is defined as **L**(*t*) = *m***r**(*t*) × **v**(*t*) and its **torque** as **τ**(*t*) = *m***r**(*t*) × **a**(*t*). Show that **L**′(*t*) = **τ**(*t*). Deduce that if **τ**(*t*) = **0** for all *t*, then **L**(*t*) is constant. (This is the *law of conservation of angular momentum*.)

To determine

**To show:** The

Explanation

**Given data:**

**Formula used:**

From differentiation rule,

Take differentiation with respect to *t* on both sides of equation (1).

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