Answered: A sprinter participating in the 200 m…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section5.3: Nonuniform Circular Motion

Problem 5.5QQ: Which of the following is impossible for a car moving in a circular path? Assume that the car is...

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Question

A sprinter participating in the 200 m dash has to run around a track that has a circular arc with a radius of curvature of 26 m. She completes the 200 m dash in 22.8 seconds at constant speed throughout the race.

a) What is the magnitude of her centripetal acceleration in m/s² as she runs the curved portion of the track?

b) What is the magnitude of her tangential acceleration in m/s² as she runs the curved portion of the track?

c) What is the magnitude of her angular acceleration in rad/s² as she runs the curved portion of the track?

d) What is the magnitude of her resultant linear acceleration in m/s² as she runs the curved portion of the track?

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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