Initial Acceleration of a Center of Mass

1. mparsons06

61
1. The problem statement, all variables and given/known data

A uniform rod of length 1.25 m is attached to a frictionless pivot at one end. It is released from rest from an angle θ = 23.0° above the horizontal.

Find the magnitude of the initial acceleration of the rod's center of mass.

2. Kenyi

1
You can use the fact that the center of mass lies at 1/2 * L and that gravity grips the rod here. You can then use a simple geometric rule to find the force perpendicular to the rod, hence its initial acceleration.

3. jeppetrost

88
You can calculate the torque exerted by gravity, and hence the angular acceleration of the rod. This can be related to the linear acceleration (of for instance the CoM) by the formula
$$\alpha D = a$$
where D is the distance to the point of interest (CoM in this example)