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So we see that, with our definition of acceleration as the rate of change of velocity, which is a
vector, a body moving at a steady speed around a circle is accelerating towards the center all
the time, although it never gets any closer to it.
If this thought makes you uncomfortable, it is
because you are still thinking that acceleration must mean a change of speed, and just changing
direction doesn’t count.
20.4
Finding the Acceleration in Circular Motion
It is possible to find an explicit expression for the magnitude of the acceleration towards the
center (sometimes called the
centripetal
acceleration) for a body moving on a circular path at
speed
v
.
Look again at the diagram above showing two values of the velocity of the cannonball
one second apart.
As is explained above, the magnitude
a
of the acceleration is the length of
the small dashed vector on the right, where the other two sides of this long narrow triangle
have lengths equal to the speed
v
of the cannonball.
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This note was uploaded on 01/08/2012 for the course PHY 322 taught by Professor Daser during the Spring '09 term at SUNY Stony Brook.
 Spring '09
 DASER
 Acceleration

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