Answered: A carousel spins at an angular velocity…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Concept explainers

Question

A carousel spins at an angular velocity of +1.2 rad/s. The brake is applied and the carousel completes exactly 7 revolutions while stopping. In rad/s², calculate the angular acceleration of the carousel as it is stopping.

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

Step 1

The initial angular velocity of the carousel $ω_{0} = 1.2 rad / s$

The final angular velocity of the carousel $ω_{f} = 0 rad / s$

The number of revolutions n= 7 revolutions .

Hence the angular displacement , $θ = 2 πn = 2 (3.14) (7) rad = 44 rad$

Step 2

The angular acceleration $α$ is calculated from the following kinematic equation

${ω_{f}}^{2} = {ω_{o}}^{2} + 2 αθ α = \frac{{ω_{f}}^{2} - {ω_{o}}^{2}}{2 θ} = \frac{{(0 rad / s)}^{2} - {(1.2 rad / s)}^{2}}{2 (44 rad)} α = - 1.64 \times 10^{- 2} rad / s^{2}$

Step by step

Solved in 3 steps

Knowledge Booster

Angular speed, acceleration and displacement

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.

Similar questions