Simple harmonic motion dash in equation

[chense]

Why is there a '-' sign in the equation

a= -w.w.y

where a is the centripetal acceleration , w is the angular velocity and y is the displacement[?]

 

[teddy]

a= -w.w.y

'-' sign is there because here 'a' is component of acceleration in the radial direction which is normally taken positive outwards.As the centripetal acceleration is towards the center its component along radial direction is negative,hence the negative sign ('w' and 'y' are positive in the above equation,'w' being the magnitude of angular velocity and 'y' being the magnitude of distance from the axis of rotation)

cheers

 

[rdt2]

Originally posted by teddy
a= -w.w.y

'-' sign is there because here 'a' is component of acceleration in the radial direction which is normally taken positive outwards.As the centripetal acceleration is towards the center its component along radial direction is negative,hence the negative sign ('w' and 'y' are positive in the above equation,'w' being the magnitude of angular velocity and 'y' being the magnitude of distance from the axis of rotation)

cheers

Chense,

Can you just clarify what you do mean here - are you talking about circular motion, in which case teddy is right. But normally one would use 'r' for the radial distance - while you used 'y' and called it 'displacement'. Which makes me think you might mean 'amplitude' of an oscillation.

Cheers,

Ron.

 

[plus]

If there wasn't a negative sign, then if it is moving forwards at a point w>0, then it will always move forwards, with increasing velocity.

Not exactly the motion of an oscillator.

 

[rdt2]

Originally posted by plus
If there wasn't a negative sign, then if it is moving forwards at a point w>0, then it will always move forwards, with increasing velocity.

Not exactly the motion of an oscillator.

My point exactly - which is why I'd like chense to clarify these terms.

Cheers,

ron.

 

[chense]

Actually, the equation I mentioned is related to simple harmonic motion, but it also has some sort of connection with circular motion. (According to the tutor who gave me the equation he used the theory behind circular motion to analyse simple harmonic motion.)

 

[rdt2]

Originally posted by chense
Actually, the equation I mentioned is related to simple harmonic motion, but it also has some sort of connection with circular motion. (According to the tutor who gave me the equation he used the theory behind circular motion to analyse simple harmonic motion.)

Got you now!

Think of the particle moving in a circular track of radius r at constant angular velocity w. Now imagine looking at the track from the side - the particle (or, more correctly, its projection) will oscillate up and down. Let's say that the instantaneous distance of the particle above or below the central axis is y. The maximum value of y will be r, which is the amplitude of the SHM.

The equation for y is:

y = r sin w.t

Differentiating twice gets you the acceleration:

a = - r.w.w sin w.t = - w.w.y

Mathematically, that's where the minus comes from. As 'plus' mentioned, its physical significance is that as the particle gets further from y = 0, then it DEcelerates (because of the minus) and comes back again.

Cheers,

Ron.