Differences between Angular, Tangential, & Centripetal Acceleration / A Tale of 3 Accelerations

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2:44 Explained in depth Tangential acceleration (at) is a result of a change in speed. Centripetal acceleration (ac) is a result of a change in direction. In a circular motion, your direction is always changing (because you're moving in a circle, duh). However, your speed (velocity) can be constant and you would still be accelerating because even though there might not be a change in velocity that's happening, a change in direction is still inevitable. Acceleration is defined as "the change in velocity". The change in "velocity" can be a change in either the speed, direction, or a change in both. Hence, acceleration occurs. And you would only be having centripetal acceleration because your direction is changing but your speed is constant, so the tangential acceleration goes goodbye. Since tangential acceleration (at) is defined as the result of a change in speed, circular motion can still work without the need of tangential acceleration.

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this Was amazing sir...... earlier I used to be very confused in all these acceleration but the way you explained it you are best sir

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An off-topic question but on a free response, if my final answer happens to have 'g' in it, should I change it to 10 m/s^2 or should I leave it as 'g'? For example, if a free response is asking me solve a problem using variables (instead of actual numbers), can I leave my answer as 1.5g or something like that?

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My advice is to, if there are only variables in the problem, leave "g" in your answer. If the free response question has numbers, then substitute in 9.81 m/s^2 for g. If they want you to use 10 m/s^2, they will tell you.

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U said tangential acceleration exist if the magnitude of velocity changes but uniform circular motion has constant magnitude of velocity.Can u explain pls😢

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Thank you so much you saved me though😊

[@FlippingPhysics]

The definition of uniform circular motion is that there is no tangential acceleration and the magnitude of the tangential velocity stays constant. (The radius also stays constant) Non-uniform circular motion and uniform circular motion are very different. www.flippingphysics.com/nonuniform-circular-motion-car.html Also, you are welcome!!

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[@anshurouniyar]

Hey u did mistake in case of tangential acceleration it's direction is changing while going up it is opposite of velocity and while going down it is along velocity

[@FlippingPhysics]

Unfortunately, I am not quite sure what you are referring to. Please watch this video, it goes into more details about the direction of tangential acceleration and velocity: www.flippingphysics.com/tangential-directions.html

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Centripetal acceleration having some magnitude doesn't make any sense. Because it's only changing direction of V but not its magnitude. Please clarify the point

[@carultch]

The velocity may be changing its direction without changing its magnitude, but there still is an acceleration, and that acceleration does have some magnitude. Khan Academy has a great visual demonstration for why this is. He plots position around a circle on plot 1, and he plots velocity components around the circle on plot 2. In the limit as we consider smaller and smaller differences in time, we can see that the changes in position around the velocity graph point inward on the position graph. Considering the change in velocity per change in time, you will see that dv/dt approaches v^2/r in the limit as dt approaches zero. The plot of the velocity vector components is called a hodograph. Velocity is tangent to the trajectory itself, while acceleration is tangent to the hodograph of the trajectory.

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but are they same in magnitude tho that's the puzzling part

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