# Why angular acceleration is positive if object rotating clockwise is slowing down?

## Main Question or Discussion Point

Hello! May i ask a question?

Why angular acceleration is positive if object rotating clockwise is slowing down?

Thanks.

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Doc Al
Mentor

What's the direction of the change in angular speed?

Another example, for linear motion: Toss a ball straight up into the air. It's moving up and slowing down, but what's the direction of its acceleration?

What's the direction of the change in angular speed?

Another example, for linear motion: Toss a ball straight up into the air. It's moving up and slowing down, but what's the direction of its acceleration?
the gravitational acceleration is always coming down.
so the ball's accel is downwards?

hmm. wait. say i define positive upwards, g is negative cos it is downwards.
the ball is deccelerating upwards so it is negative?

Doc Al
Mentor

the gravitational acceleration is always coming down.
so the ball's accel is downwards?
Right.
hmm. wait. say i define positive upwards, g is negative cos it is downwards.
Right.
the ball is deccelerating upwards so it is negative?
The ball is moving upwards, but slowing down. So its acceleration is negative (downwards).

(If the acceleration was in the same direction as the velocity--upwards in this case--its speed would be increasing. That's what happens on the way down: both velocity and acceleration point downwards, so it speeds up.)

hmm okay! now i understand. but how abt an object rotating clockwise is slowing down?

when it rotates clockwise, its angular speed is negative right?
i not sure the direction of angular speed as it is not stated in my notes.

my notes just say " angular acceleration is positive if object rotating counterclockwise is speeding up and angular acceleration is positive if object rotating clockwise is slowing down"

alxm

If you have a right-handed coordinate system, then counterclockwise directions are positive and clockwise directions are negative.

If something is speeding up, then its acceleration is in the direction of motion. If it's slowing down, its acceleration is opposite the direction of motion.

Doc Al
Mentor

but how abt an object rotating clockwise is slowing down?
So which direction is its acceleration? Clockwise or counterclockwise? Then you can decide whether it should be called positive or negative.
when it rotates clockwise, its angular speed is negative right?
i not sure the direction of angular speed as it is not stated in my notes.
The usual convention is that counterclockwise is positive and clockwise is negative.

my notes just say " angular acceleration is positive if object rotating counterclockwise is speeding up and angular acceleration is positive if object rotating clockwise is slowing down"
This is true.

hmm. why " angular acceleration is positive if object rotating counterclockwise is speeding up and angular acceleration is positive if object rotating clockwise is slowing down" is true?

say i use the normal convention, clockwise is negative. why angular accel of obj rotating clockwise slowing down is positive?

Doc Al
Mentor

hmm. why " angular acceleration is positive if object rotating counterclockwise is speeding up and angular acceleration is positive if object rotating clockwise is slowing down" is true?

A) If something rotating counterclockwise speeds up, which way is it accelerating? Clockwise or counterclockwise?

B) If something rotating clockwise slows down, which way is it accelerating? Clockwise or counterclockwise?

Then use the sign convention to determine whether it's positive or negative.

A) If something rotating counterclockwise speeds up, which way is it accelerating? Clockwise or counterclockwise?

B) If something rotating clockwise slows down, which way is it accelerating? Clockwise or counterclockwise?

Then use the sign convention to determine whether it's positive or negative.
A) it is accelerating counterclockwise as well so it is positive?

B) it is decelerating in clockwise direction (negative). which means it is accelerating in counterclockwise direction and so it is positive as well?

Doc Al
Mentor

A) it is accelerating counterclockwise as well so it is positive?

B) it is decelerating in clockwise direction (negative). which means it is accelerating in counterclockwise direction and so it is positive as well?
Sounds good, but with some comments. Careful with the term "decelerating"--I find it more confusing than helpful. (It just means "slowing down".) Much better to stick with acceleration, which can be positive or negative. So for B I would say it's moving clockwise but slowing down (decelerating), thus the acceleration is counterclockwise and thus positive.

i see.. yay! okay. i get it!! thanks a lot! thanks thanks :):):)