Answer to Question #152737 in Classical Mechanics for GuardianVex

Question

38. An electron of mass ‘m’ moves with a uniform speed v around the nucleus along a
circular path of radius R.
a) Derive an expression for the acceleration of the electron.
b) Is this acceleration a constant vector? Why?
c) Explain why the speed of electron does not increase even though it is accelerated by
the above acceleration.

Answer 1

a)

$a=\frac{mv^2}{R}$

b)

Acceleration is constant in absolute value and not constant in direction.

c)

The object has a constant speed, its direction is always changing. This change in velocity is caused by an acceleration, whose magnitude is

held constant, but whose direction also is always changing.