Explanation Given Information: The three dimensional motion of a particle is defined by the position vector r = ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k . Calculation: Write three-dimensional motion of particle in term of position vector equation. r = ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k Write the expression for velocity using the relation: v = d r d t Substitute ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k for r . v = d ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k d t = R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k Write the expression for acceleration using the relation: a = d v d t Substitute R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k for v . a = d ( R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k ) d t = R ( − ω n sin ω n t − ω n sin ω n t − ω n 2 t cos ω n t ) i + R ( 2 ω n cos ω n t − ω n 2 t sin ω n t ) k = ω n R ( − ( 2 sin ω n t + ω n t cos ω n t ) i + ( 2 cos ω n t − ω n t sin ω n t ) k ) (1) Calculate the velocity ( v ) of the particle. v 2 = v x 2 + v y 2 + v z 2 Substitute R ( cos ω n t − ω n sin ω n t ) for v x , c for v y and R ( sin ω n t + ω n t cos ω n t ) for v z

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 11.5, Problem 11.151P

To determine

The radius (ρ) of curvature of the path described by the particle when time (t) is 0 sec.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 11.150P

Chapter 11.5, Problem 11.152P

Students have asked these similar questions

Please show All work and fill it in thermodynamics

Quick solution required. My request, Don't use Ai. Mechanical engineering

Please give handwritten solution, don't use chatgpt. Fbd should be included

Chapter 11 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

Ch. 11.1 - A bus travels the 100 miles between A and B at 50...Ch. 11.1 - Two cars A and B race each other down a straight...Ch. 11.1 - A snowboarder starts from rest at the top of a...Ch. 11.1 - The motion of a particle is defined by the...Ch. 11.1 - The vertical motion of mass A is defined by the...Ch. 11.1 - A loaded railroad car is rolling at a constant...Ch. 11.1 - A group of hikers uses a GPS while doing a 40-mile...Ch. 11.1 - The motion of a particle is defined by the...Ch. 11.1 - A girl operates a radio-controlled model car in a...Ch. 11.1 - The motion of a particle is defined by the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The radius ( ρ ) of curvature of the path described by the particle when time ( t ) is 0 sec.

Solution Summary: The author describes the three-dimensional motion of a particle defined by the position vector r=(rho ).

Concept explainers

Videos

The radius (ρ) of curvature of the path described by the particle when time (t) is 0 sec.

Want to see the full answer?

Chapter 11 Solutions