Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN: 9781133939146

Author: Katz, Debora M.

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth w…

Videos

Textbook Question

Chapter 12, Problem 31PQ

A disk is initially at rest. A penny is placed on it at a distance of 1.0 m from the rotation axis. At time t = 0 s, the disk begins to rotate with a constant angular acceleration of 2.0 rad/s² around a fixed, vertical axis through its center and perpendicular to its plane. Find the magnitude of the net acceleration of the coin at t = 1.5 s.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12, Problem 30PQ

Chapter 12, Problem 32PQ

Students have asked these similar questions

Question B3 Consider the following FLRW spacetime: t2 ds² = -dt² + (dx² + dy²+ dz²), t2 where t is a constant. a) State whether this universe is spatially open, closed or flat. [2 marks] b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. [3 marks] c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A. d) The Friedmann equations are 2 k 8πG а 4πG + a² (p+3p). 3 a 3 [5 marks] Use these equations to determine the energy density p(t) and the pressure p(t) for the FLRW spacetime specified at the top of the page. [5 marks] e) Given the result of question B3.d, state whether the FLRW universe in question is (i) radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv) none of the previous. Justify your answer. f) [5 marks] A conformally…

SECTION B Answer ONLY TWO questions in Section B [Expect to use one single-sided A4 page for each Section-B sub question.] Question B1 Consider the line element where w is a constant. ds²=-dt²+e2wt dx², a) Determine the components of the metric and of the inverse metric. [2 marks] b) Determine the Christoffel symbols. [See the Appendix of this document.] [10 marks] c) Write down the geodesic equations. [5 marks] d) Show that e2wt it is a constant of geodesic motion. [4 marks] e) Solve the geodesic equations for null geodesics. [4 marks]

Page 2 SECTION A Answer ALL questions in Section A [Expect to use one single-sided A4 page for each Section-A sub question.] Question A1 SPA6308 (2024) Consider Minkowski spacetime in Cartesian coordinates th = (t, x, y, z), such that ds² = dt² + dx² + dy² + dz². (a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V. (b) Consider now the coordinate system x' (u, v, y, z) such that u =t-x, v=t+x. [2 marks] Write down the line element, the metric, the Christoffel symbols and the Riemann curvature tensor in the new coordinates. [See the Appendix of this document.] [5 marks] (c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify explicitly that V. V is invariant under the coordinate transformation. Question A2 [5 marks] Suppose that A, is a covector field, and consider the object Fv=AAμ. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. [5 marks] (b)…

Chapter 12 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 12.1 - Figure 12.5 shows two rotating objects. Indicate...Ch. 12.2 - Prob. 12.2CE Ch. 12.2 - Prob. 12.3CE Ch. 12.2 - Prob. 12.4CE Ch. 12.2 - Prob. 12.5CE Ch. 12.5 - For each exercise shown in Figure 12.22, how does...Ch. 12 - Often, we model the Moon as a particle in a...Ch. 12 - Suppose a satellite orbits the Earth such that it...Ch. 12 - Prob. 3PQ Ch. 12 - Prob. 4PQ

Ch. 12 - A ceiling fan is rotating counterclockwise with a...Ch. 12 - As seen from above the Earths North Pole, the...Ch. 12 - A rotating objects angular position is given by...Ch. 12 - A rotating objects angular position is given by...Ch. 12 - Jupiter rotates about its axis once every 9 hours...Ch. 12 - Prob. 10PQ Ch. 12 - Prob. 11PQ Ch. 12 - Prob. 12PQ Ch. 12 - Prob. 13PQ Ch. 12 - Prob. 14PQ Ch. 12 - Prob. 15PQ Ch. 12 - A disk rolls up an inclined plane as shown in...Ch. 12 - Jeff, running outside to play, pushes on a...Ch. 12 - A potters wheel rotating at 240 rev/min is...Ch. 12 - Friction in an old clock causes it to lose 1...Ch. 12 - A wheel starts from rest and in 12.65 s is...Ch. 12 - Prob. 21PQ Ch. 12 - Starting from rest, a wheel reaches an angular...Ch. 12 - A potters wheel is rotating with an angular...Ch. 12 - The angular speed of a wheel is given by (t) =...Ch. 12 - Prob. 25PQ Ch. 12 - Prob. 26PQ Ch. 12 - An electric food processor comes with many...Ch. 12 - Prob. 28PQ Ch. 12 - A bicyclist is testing a new racing bike on a...Ch. 12 - Prob. 30PQ Ch. 12 - A disk is initially at rest. A penny is placed on...Ch. 12 - Prob. 32PQ Ch. 12 - Consider again the two wind turbines in Problem...Ch. 12 - Consider again the two wind turbines in Problem...Ch. 12 - In testing an automobile tire for proper...Ch. 12 - Prob. 36PQ Ch. 12 - A merry-go-round at a childrens park begins at...Ch. 12 - A wheel rotating at a constant rate of 1850...Ch. 12 - Why are doorknobs placed on the edge opposite the...Ch. 12 - Prob. 40PQ Ch. 12 - Prob. 41PQ Ch. 12 - Prob. 42PQ Ch. 12 - A wheel of inner radius r1 = 15.0 cm and outer...Ch. 12 - A uniform plank 6.0 m long rests on two supports,...Ch. 12 - Prob. 45PQ Ch. 12 - Prob. 46PQ Ch. 12 - Prob. 47PQ Ch. 12 - Prob. 48PQ Ch. 12 - Prob. 49PQ Ch. 12 - Prob. 50PQ Ch. 12 - Prob. 51PQ Ch. 12 - Given a vector A=4.5+4.5j and a vector B=4.5+4.5j,...Ch. 12 - A square plate with sides 2.0 m in length can...Ch. 12 - Prob. 54PQ Ch. 12 - A disk with a radius of 4.5 m has a 100-N force...Ch. 12 - Disc jockeys (DJs) use a turntable in applying...Ch. 12 - Prob. 57PQ Ch. 12 - Prob. 58PQ Ch. 12 - A wheel initially rotating at 85.0 rev/min...Ch. 12 - Prob. 60PQ Ch. 12 - A centrifuge used for training astronauts rotating...Ch. 12 - Problems 62 and 63 are paired. 62. C A disk is...Ch. 12 - Prob. 63PQ Ch. 12 - A potters wheel rotates with an angular...Ch. 12 - Prob. 65PQ Ch. 12 - Prob. 66PQ Ch. 12 - Prob. 67PQ Ch. 12 - Lara is running just outside the circumference of...Ch. 12 - The propeller of an aircraft accelerates from rest...Ch. 12 - A ball rolls to the left along a horizontal...Ch. 12 - Three forces are exerted on the disk shown in...Ch. 12 - Consider the disk in Problem 71. The disks outer...Ch. 12 - Prob. 73PQ Ch. 12 - Prob. 74PQ Ch. 12 - Prob. 75PQ Ch. 12 - Prob. 76PQ Ch. 12 - Prob. 77PQ Ch. 12 - Prob. 78PQ Ch. 12 - Prob. 79PQ Ch. 12 - Prob. 80PQ Ch. 12 - If the rod in Problem 79 is in equilibrium, what...Ch. 12 - As a compact disc (CD) spins clockwise as seen...Ch. 12 - A disk-shaped machine part has a diameter of 40.0...Ch. 12 - Prob. 84PQ

Knowledge Booster

Learn more about

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

Solution Summary: The author explains the magnitude of the net acceleration of a coin, and the expressions for centripetal and tangential acceleration.

Concept explainers

Videos

Want to see the full answer?

Chapter 12 Solutions