Uniform Circular motion.1. Mini Lecture2. Let the position of a particle be given by:(t) = Rcos (wt)i + Rsin (wt)j3. Calculate the expression for the velocityvector and show that the velocity vector istangential to the circumference of the circle.4. Calculate the expression for the accelerationvector and show that the acceleration vectorpoints radially inward.5. Calculate the magnitude of the velocity andmagnitude of the acceleration, and thereforeshow thatv2a =R

if doubt arises please mention in the comments.

Answered: Uniform Circular motion. 1. Mini…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter15: Place And Time

Section: Chapter Questions

Problem 6AYK

See similar textbooks

Similar questions

A race car travels 825 km around a circular sprint track of radius 1.313 km. How many times did it go around the track?
(a) If AF=BF , can we conclude A=B ? (b) If AF=BF , can we conclude A=B ? (c) If FA=BF , can we conclude A=B ? Why or why not?
Carolyn rides her bike 40.0 south of west for 5.40 miles as illustrated in Figure P3.25. What is the distance she would have to ride due south and due west to reach the same location?
Two planets in circular orbits around a star have speed of v and 2v . (a) What is the ratio of the orbital radii of the planets? (b) What is the ratio of their periods?
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in Figure P7.15. The length of the arc ABC is 235 m, and the car completes the turn in 36.0 s. (a) Determine the cars speed. (b) What is the magnitude and direction of the acceleration when the car is at point B? Figure P7.15
Two birds begin next to each other and then fly through the air at the same elevation above level ground at 22.5 m/s. One flies northeast, and the other flies northwest. After flying for 10.5 s, what is the distance between them? Ignore the curvature of the Earth.
A child is practicing for a BMX race. His speed remains constant as he goes counterclockwise around a level track with two nearly straight sections and two nearly semicircular sections, as shown in the aerial view of Figure CQ7.12. (a) What are the directions of his velocity at points A, B, and C? For each point, choose one: north, south, east, west, or nonexistent, (b) What are the directions of his acceleration at points A, B, and C? Figure CQ7.12
between points in a plane do not change when a coordinate system is rotated In other words, the magnitude of a vector Is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle to become a new coordinate system S’, as shown in the following figure. A point in a plane has coordinates (x,y)in S and coordinates (x,y) in S’. (a) Show that, during the transformation of rotation, the coordinates in S are expressed in terms of the coordinates in S by the following relations: {x=xcos+ysiny=xsin+ycos (b) Show that the distance of point Pto the origin is invariant under rotations of the coordinate system. Here, you have to show that x2+y2=x2+y2. (c) Show that the distance between points Pand Q is invariant under rotations of the coordinate system. Here, you have to show that ( xP =xQ )2+( yP yQ )2=( xP =xQ )2+( yP yQ )2 .
A person drives a car around a circular, level cloverleaf with a radius of 70 m at a uniform speed of 10 m/s. (a) What is the acceleration of the car? (b) Compare this answer with the acceleration due to gravity as a percentage. Would you be able to sense the cars acceleration if you were riding in it?
A particle moves along a path, and its speed increases with time. (i) In which of the following cases are its acceleration and velocity vectors parallel? (a) when the path is circular. (b) when the path is straight. (c) when the path is a parabola. (d) never. (ii) From the same choices, in which case are its acceleration and velocity vectors perpendicular everywhere along the path?
A velocity vector has a magnitude of 720 m/s. Two students draw arrows representing this vector. Clarisse chooses a scale such that 1 cm 100 m/s. a. What is the length of the arrow that Clarisse draws? b. Francoiss arrow is half as long as Clarisses. What is Francoiss scale? c. Is one students choice better than the other? If so, what makes it a better scale?
Peter throws a baseball through a houses window. He stands 3.4 m from the window. The ball starts in his hand 1.1m above the ground and goes through the window at a point 2.4 m off the ground. a. Sketch the problem, including an xy coordinate system with the origin on the ground directly below the initial position of the ball, the y axis pointing upward, and the x axis pointing toward the house. b. What are the initial and final coordinates of the ball?

SEE MORE QUESTIONS

Recommended textbooks for you

An Introduction to Physical Science

Physics

ISBN:

9781305079137

Author:

James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:

Cengage Learning

Physics for Scientists and Engineers: Foundations…

Physics

ISBN:

9781133939146

Author:

Katz, Debora M.

Publisher:

Cengage Learning

University Physics Volume 1

Physics

ISBN:

9781938168277

Author:

William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:

OpenStax - Rice University

An Introduction to Physical Science

Physics

ISBN:

9781305079137

Author:

James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:

Cengage Learning

Physics for Scientists and Engineers: Foundations…

Physics

ISBN:

9781133939146

Author:

Katz, Debora M.

Publisher:

Cengage Learning

University Physics Volume 1

Physics

ISBN:

9781938168277

Author:

William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:

OpenStax - Rice University

College Physics

Physics

ISBN:

9781305952300

Author:

Raymond A. Serway, Chris Vuille

Publisher:

Cengage Learning

College Physics

Physics

ISBN:

9781285737027

Author:

Raymond A. Serway, Chris Vuille

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS