How Does an Object Moving in a Circle at Constant Speed Accelerate?

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SUMMARY

An object moving in a circle at constant speed experiences acceleration due to the continuous change in direction, despite maintaining a constant speed. The correct answer to the homework question is D: the object changes velocity but not speed. The radial acceleration, calculated using the formula Arad=V²/R, indicates that while the speed remains constant, the direction of the velocity vector changes, resulting in acceleration. Option B is incorrect because acceleration is not constant in magnitude; it is constant in direction but varies with the change in the velocity vector's orientation.

PREREQUISITES
  • Understanding of vector quantities in physics
  • Familiarity with circular motion concepts
  • Knowledge of the formula for radial acceleration (Arad=V²/R)
  • Basic principles of velocity and acceleration
NEXT STEPS
  • Study the principles of centripetal force in circular motion
  • Learn about the relationship between speed, velocity, and acceleration
  • Explore the concept of angular velocity and its implications
  • Investigate real-world applications of circular motion, such as in amusement park rides
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding the dynamics of circular motion and acceleration.

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Homework Statement



Acceleration is a vector representing the rate of change of velocity. An object moving in a circle at constant speed:

A. accelerates without changing its velocity
B. Has constant acceleration
C. Changes speed but not velocity
D. Changes velocity but not speed


Homework Equations



Arad=V2/R


The Attempt at a Solution



The answer given in my book is D, which makes sense, but I also don't see how B is wrong. If the object's speed is constant, and radial acceleration is based off the magnitude of velocity (hence changing direction of velocity doesn't affect it), then shouldn't the acceleration also be constant?
 
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Remember that acceleration is a vector; it has a direction.
 

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