### General Rotation of a Rigid Body

• Solve problems in two-dimensional rigid-body dynamics, regardless of their kinematic characteristics, by equating the sum of the forces acting on the rigid body to the vectors ma and Ia. To effect this solution, construct appropriate free-body diagrams.

For rigid body rotation $\theta$ $\omega = \dfrac{d\theta}{dt}$ $\alpha = \dfrac{d\omega}{dt}$ $\alpha d\theta = \omega d\omega$

### Solved Example:

#### 33-1-01

Two objects are sitting on a rotating turntable. One is much further out from the axis of rotation. Which one has the larger angular velocity?

Solution:
Angular velocity depends upon angular displacement covered in unit time. Irrespective of the location of the objects, the angular displacement is same, hence there angular velocities are same. (Hoever, their linear velocities will be different.)

### Solved Example:

#### 33-1-02

What is the Moment of Inertia of a thin rod of mass 'M&' and length 'L' about an axis perpendicular to the rod at its mid-point? (SSC Scientific Asst Nov 2017 Shift II)