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 f
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 triangl
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
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.
Cl
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,
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
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
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.
Su
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 w
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