Answered: An amusement park ride rotates around a…

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)...

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Question

An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt² – ct³ where a = 1.9 rad, b = 0.75 rad/s² and c = 0.025 rad/s³.

Randomized Variables

a = 1.9 rad
b = 0.75 rad/s²
c = 0.025 rad/s³

^{1) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t₁?}

^{2) Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values.}

^{3) What is the angular acceleration in rad/s2 when the ride is at rest at t = t₁?}

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 .

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