Assumptions - Circular Motion
The applet simulates the velocity, acceleration, and the radial
(centripetal) and tangential components of the acceleration
of a mass point performing circular motion.
This is a theoretical applet that does not involve any physical
assumptions. However, some notation and terminology, some of
which may be unconventional, is explained below.
- v(0)-slider. The quantity v whose
initial value at time t = 0 can be set with this slider is
called "circle velocity" in the documentation. v(t)
is a scalar quantity equal to the speed of the mass point at time
t except for a possible minus sign. The quantity is
negative if the motion of the mass point is in the clockwise sense
(negative sense of revolution) and positive if in the
counter-clockwise sense (positive sense of revolution).
The absolute value of the circle velocity v is equal to
the particle's speed.
- dv/dt(0)-slider. The quantity
dv/dt whose initial value at time t = 0 can
be set with this slider is the time-rate-of-change of the "circle
velocity". dv/dt(t) can take on both
positive and negative values, positive if v is increasing
at time t and negative if v is decreasing.
The absolute value of dv/dt is equal to the
absolute value of the tangential component of the mass point's
acceleration and denoted atan in the applet.
- w(0)-slider. The
quantity w (Greek letter; read: omega)
whose initial value at time t = 0 can be set with this
slider is the angular velocity of the mass point. w(t) can take on both positive and
negative values, positive for counter-clockwise motion (positive
sense of revolution) and negative for clockwise motion (negative
sense of revolution).
- a(0)-slider. The quantity
a (Greek letter; read: alpha) whose
initial value at time t = 0 can be set with this slider is
called angular acceleration. It is the time-rate-of-change
of the angular velocity, a =
dw/dt. a(t) can take on both positive and
negative values, positive if w is
increasing at time t and negative if w is decreasing.