Please wait for the animation to completely load.

How would you describe the motion of the object shown
**(position is given in meters and time is given in seconds)**?
Restart. The object is moving in a circle about x = 0 m and y = 0
m, but the object's x and y coordinates vary with time. They vary in a special
way such that x and y are always between -1 m and 1 m. To see this, look at
Animation 2
and watch the x and y values change in the table. This is called the component form.
We can also describe the motion in terms of the vector form. In this case, the
radius vector, **r**, always has a magnitude of 1 m. but it
changes direction. Look at
Animation 3. We describe the direction of this vector in terms of the angle
it makes with the positive x axis. Therefore the angle—when measured in
degrees—varies from 0 to 360. It is often convenient to give the angle
in a unit different than degrees. We call this unit a radian. The radian unit
is defined as 2π radians = 360°. Notice that both units are defined
in terms of one full revolution. To see the angle given in radians look at
Animation 4.

So why use radians? Well, it turns out that there is a really nice relationship between
angle in radians (θ), the radius (r), and the arc of the circle (s). This
geometric relationship states that: θ = s/r. Why is this useful? It allows
us to treat circular motion like one-dimensional motion. The arc is the linear
distance traveled, which is s = vt when the motion is uniform. This means that
θ = (v/r) t, since s = rθ. We call v/r by the name omega, ω,
and it is the angular velocity. Therefore, θ = ωt, for motion with
a constant angular velocity. When there is a constant angular acceleration, we
call it by the name alpha, α, and it is related to the tangential acceleration
by a_{t}/r. So when we are using radians we can use our one-dimensional
kinematics formulas with x → θ, v → ω, and a → α.

Illustration authored by Mario Belloni and Wolfgang Christian.

HTML updated for JavaScript by Ricky Davidson.

Physlets were developed at Davidson College and converted from Java to JavaScript
using the
SwingJS
system developed at St. Olaf College.