Acceleration in Circular Motion

AI Thread Summary
The acceleration of an object in uniform circular motion is directed towards the center of the circle and has a magnitude of ω²r. This inward acceleration occurs because the object's speed remains constant, meaning there is no force acting in the direction of motion. To visualize this, drawing a vector triangle can help illustrate the change in velocity as the object moves along the circular path. The relationship between linear velocity and angular velocity, expressed as v = ωr, is crucial for understanding the acceleration. Overall, the discussion emphasizes the importance of centripetal acceleration in maintaining circular motion.
Emz19
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Could anyone help my with proving that the acceleration of an object that is moving with uniform circular motion is directed towards the centre of the circle and is of magnitude ω^2(r). Thanks
 
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Directed towards centre because motion is uniform, so speed constant, which means no force in direction of motion. Has to be in not out in order to "push" the object round in a circle.

For the magnitude... try drawing a vector triangle showing the change in velocity for a small distance moved around the circle - the 3 sides of the triangle being the initial velocity, the final velocity (the velocity after moving a small distance around), and the change in the velocity. Then you have a velocity change, and remember that acceleration is change in velocity per unit time. And you know know the relation between velocity and angular velocity: v = ωr. That should be enough information to get there...

Hope this helps!
 
That is great, thanks a million! It is much clearer to visualise now. :)
 
Thanks jtbell, just had a look at the link and this is also really helpful. Thanks a mill :)
 

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