# difference between angular, tangential and centripital acceleration

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• Apr 17th 2010, 07:44 PM
superdude
difference between angular, tangential and centripital acceleration
I’m having trouble getting my head around the difference between the different types of acceleration involved in circular motion.
So tangential acceleration $\displaystyle a_t$ is similar to the most common type of acceleration, such as a car accelerating in a straight line. Tangential acceleration is always tangent to the circle being traced by the objects motion.
Angular acceleration $\displaystyle \alpha$ is the derivative of the angular velocity with respect to time. So angular velocity is the rate at which an object completes the path around the circle and this means angular acceleration is how this is changing. I have no clue what direction this would be in.
Centripetal acceleration $\displaystyle a_c$ is always directed to the center of the circle. I don’t really see how this arises. Can this be measure directly?
Are all types of acceleration a vector?

for example, I would've thought that a satellite orbiting the Earth has tangential acceleration, but it has centripetal acceleration.
• Apr 18th 2010, 05:56 AM
hollywood
Tangential and angular acceleration are two different ways of expressing the same thing - that the object is going around the circle slower or faster. The tangential acceleration is equal to the radius times the angular acceleration.

Centripetal acceleration is what keeps the motion circular - without it, the object would go in a straight line. There is an equation that relates it to the angular (or tangential) velocity.

The only force acting on a satellite in a circular orbit is gravity, which is toward the Earth, so the satellite has only centripetal acceleration. It goes around the Earth at a constant speed, so the tangential acceleration is zero.

If the satellite fires its rockets, it can have tangential acceleration for a time.

Hope this helps. Post again if you have any questions.

- Hollywood
• Apr 18th 2010, 02:30 PM
superdude
That helps, but I'm still uneasy with centripetal.Centripital force is always pointing towards the centre of the circle right? So I assumed that the centripetal acceleration is also pointing towards the centre of the circle, is that correct? If yes then how come a satellite orbits the Earth instead of being accelerated towards the centre of it, if it's undergoing centripetal acceleration?
• Apr 18th 2010, 02:41 PM
skeeter
Quote:

Originally Posted by superdude
That helps, but I'm still uneasy with centripetal.Centripital force is always pointing towards the centre of the circle right? So I assumed that the centripetal acceleration is also pointing towards the centre of the circle, is that correct? If yes then how come a satellite orbits the Earth instead of being accelerated towards the centre of it, if it's undergoing centripetal acceleration?

since $\displaystyle \vec{F_c} = m\vec{a_c}$ , centripetal force and acceleration always have the same direction.

if the satellite did not have a sufficient magnitude of tangential velocity, it would fall back to Earth. Centripetal acceleration is perpendicular to the satellite's velocity.

Experiment yourself ... tie a ball to the end of a string and whirl it in a circle ... what force keeps the ball moving in a circle? what happens to the ball if you let loose the string?