Starting from rest, a person pedals a bicycle such that the angular acceleration of the wheels is a constant 1.70 rad/s2. The bicycle wheels are 38.5 cm in radius.(a) What is the magnitude of the bicycle's linear acceleration (in m/s2)?____m/s2(b) What is the angular speed of the wheels (in rad/s) when the linear speed of the bicyclist reaches 11.4 m/s?____rad/s(c) How many radians have the wheels turned through in that time?____rad(d) How far (in m) has the bicycle traveled in that time?_____m

Speed =Distance Time Velocity =DisplacementTime Acceleration=Change in velocityTime Angular velocity =Angular displacementTime Angular acceleration =Change in angular velocityTime (given) Radius of bicycle wheels = 38.5 cm = 0.385 m Angular acceleration of the wheel = 1.70 rad/s2 Acceleration: a = rα = (0.385 m)(1.70 rad/s2) = 0.6545 m/s2 Answer: Linear acceleration = 0.65 m/s2 Relation between linear velocity and angular velocity is v =rω Angular speed of the wheels: ω=vr =11.40.385 =29.61 rad/s Answer: Angular speed of the wheels is 29.61 rad/s.

Answered: Starting from rest, a person pedals 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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Starting from rest, a person pedals a bicycle such that the angular acceleration of the wheels is a constant 1.70 rad/s². The bicycle wheels are 38.5 cm in radius.

(a) What is the magnitude of the bicycle's linear acceleration (in m/s²)?

____m/s²

(b) What is the angular speed of the wheels (in rad/s) when the linear speed of the bicyclist reaches 11.4 m/s?

____rad/s

____rad

(d) How far (in m) has the bicycle traveled in that time?

_____m

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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