Angular acceleration, tangential acceleration
If the boards angular velocity is changing with time, then it has an angular acceleration,
defined by:
and similarly, a point on the board, a distance r from the center of rotation will possess a
tangential ac
Calculating
Consider the following equilateral triangle (side length 1.5m), with m1 = 1kg, m2 = 2kg,
and m3 = 3kg.
What is the moment of inertia about an axis passing through the center of the triangle?
The center is shown below. The radii r1, r2, r3 are
Calculating I for a board about its center
What is the moment of inertia of such uniform board about its center? Then we put O at
the center, and measure distances from there.
In similar fashion, one can calculate the moment of inertia of other objects.
E
Angular Kinematics
We have seen that forces can cause an object to move from one place to another. This is
called translation. But this is not the whole story, for consider the following situation.
Clearly the net force on the board is 0. And so the board
Distance through which the Earth rotates around Sun
Lets the distance the Earth rotates about the Sun. The Earth travels in a circle,
approximately, about the Sun. After one complete revolution, then, it has rotated through
an angle 2. Therefore it has tr
Consider an equilateral triangle. Let m1 = m2 = m3 = m out of simplicity. Where is the
center of mass? Well take the origin of our coordinates to be m1 again.
Its at,
Example
Consider a uniform board of length . Where is the center of mass?
We have,
which
What is the velocity of the center of mass of the object below. Suppose m1 = 1kg, m2 =
2kg.
Well,
Example:
Suppose you (m = 70kg) are sitting on one end of a 50kg boat 3m long, in a lake. And
you see a turtle sitting on a rock about 25cm away from the oth
systems of objects
We have seen that forces can cause an object to move from one place to another. This is
called translation. But this is not the whole story, for consider the following situation.
Suppose we have two equal and opposite forces acting on a
Angular Dynamics
When we studied translational dynamics, we wrote down N2L, which described the
relationship between the forces on an object and its translational acceleration, a. In this
section we will end up writing down the equation which describes th
Parallel axis theorem
If we calculate the moment of inertia of an object about an axis going through its center
of mass, then we can get it about any other axis parallel to it. Consider a weird object,
with a certain moment of inertia Icm about its center