# Linear acceleration in a circular path

Hi,
What is the linear acceleration of a body moving in a circular path?
its written in my book that its zero since the magnitude of velocity is constant

BUT the direction is changed so it can't be zero so this didn't persuade me.

Also I DUNNO the difference between the linear acceleration and the centripetal acceleration in a circular motion.

Thanks

Doc Al
Mentor
If the speed is constant then the tangential acceleration would be zero. But the total acceleration, which would be centripetal, would certainly not be zero. Some books use 'linear acceleration' to mean 'tangential acceleration'. (I wouldn't.)

mmm wat is the tangential acceleration?and why it is zero in case of uniform velocity while the direction is changed?and how to calculate it?

the tangential acceleration is the change of velocity of an object as it moves in a line that is tangent to the circular path its moving in right?

so since the centripetal force is tangent to the direction of velocity then it wouldn't change its magnitude , thus if the rope is cut the body will move with a constant tangential velocity yet no tangential acceleration

Right?

Doc Al
Mentor
the tangential acceleration is the change of velocity of an object as it moves in a line that is tangent to the circular path its moving in right?
For something moving in a circle, the acceleration can have two components: One component tangent to the circle, which determines the change in speed; The other component is the centripetal acceleration, due to the changing direction.
so since the centripetal force is tangent to the direction of velocity
The centripetal force is perpendicular to the direction of the velocity.

Ok thanks ,
the tangential acceleration is zero according to the law of inertia " A body retains its state of rest or motion in a straight line WITH UNIFORM VELOCITY unless acted upon by external force"

right?
Thanks

Doc Al
Mentor
No, not right. Something moving in a circle with uniform speed has zero tangential acceleration because the speed is constant, but it is definitely accelerating and there is definitely an external force acting (the centripetal force).

k.....What is the tangential acceleration?

Imagine you have a very large racing track which is in the shape of a circle, and you have a nice racing car on the track.
You get in your car and drive around the circular track at exactly 50km/hr. You look at your speedometer and it says 50, and it stays on 50 all the time.
You say to yourself, "my car has constant speed, it is not accelerating".
Your co-driver sitting next to you has done some physics and reminds you that it is not perfectly true, because the car is going round in a circle.
He points out that in order to do that you need a constant force directed towards the centre of the circle, the centripetal force, and this is provided by the grip of the wheels on the road. Your friend also points out that this force produces an acceleration towards the centre of the circle called centripetal acceleration.
You thank him for reminding you and then decide to put your foot down on the gas and make the car go faster. Your speed goes up to 100km/hr but you make sure you stay on the track.

Doc Al
Mentor
k.....What is the tangential acceleration?
Acceleration is a vector; it has direction. You can specify the acceleration in terms of its components. A component tangential to the circle (along the direction of motion) and a component perpendicular to that one along the radius of the circle (that's the "centripetal" acceleration).

No, not right. Something moving in a circle with uniform speed has zero tangential acceleration because the speed is constant, but it is definitely accelerating and there is definitely an external force acting (the centripetal force).

but i mean when we let the stone go

Imagine you have a very large racing track which is in the shape of a circle, and you have a nice racing car on the track.
You get in your car and drive around the circular track at exactly 50km/hr. You look at your speedometer and it says 50, and it stays on 50 all the time.
You say to yourself, "my car has constant speed, it is not accelerating".
Your co-driver sitting next to you has done some physics and reminds you that it is not perfectly true, because the car is going round in a circle.
He points out that in order to do that you need a constant force directed towards the centre of the circle, the centripetal force, and this is provided by the grip of the wheels on the road. Your friend also points out that this force produces an acceleration towards the centre of the circle called centripetal acceleration.
You thank him for reminding you and then decide to put your foot down on the gas and make the car go faster. Your speed goes up to 100km/hr but you make sure you stay on the track.