1. ROTATIONAL DYNAMICS

2. ROTATIONAL DYNAMICS AND MOMENT OF INERTIA  A Force applied to an object can cause it to rotate.  Lets assume the F is applied at 90 0  torque causes an angular acceleration.  Force cause linear acceleration © 2015 Pearson Education, Inc.

3. ROTATIONAL DYNAMICS AND MOMENT OF INERTIA  Moment of Inertia – How the mass of the object is distributed from the axis of rotation  M = mass of particle  r = distance away from axis of rotation  Units: kg* m 2  2 nd Law of Motion:

4. INTERPRETING THE MOMENT OF INERTIA  The moment of inertia is the rotational equivalent of mass.  An object’s moment of inertia depends not only on the object’s mass but also on how the mass is distributed around the rotation axis. © 2015 Pearson Education, Inc.

5. EXAMPLE  Find the moment of inertia for figure A.

6.  Find the moment of inertia in figure B

7. Here is a sculpture that consists of three small, heavy spheres attached by very lightweight (massless) 10-cm-long rods as shown in FIGURE 7.36. The spheres have masses m 1 = 1.0 kg, m 2 = 1.5 kg, and m 3 = 1.0 kg. What is the object’s moment of inertia if it is rotated about axis A? About axis B? EXAMPLE CALCULATING THE MOMENT OF INERTIA

8. THE MOMENTS OF INERTIA OF COMMON SHAPES © 2015 Pearson Education, Inc.

10. EXAMPLE  A mass of 2.5kg is attached to a rope that is wrapped around a pulley. The pulley has a mass of 4kg and a diameter of 60cm. How long will it take for the mass to fall 1m?

11. EXAMPLE  A 2kg, 30cm diameter disk is spinning at 300rpm. What force of friction is needed to bring the disk to rest in 3sec?

12. EXAMPLE  A 1.5 kg block is attached to a rope over a 2kg, 50cm diameter pulley frictionless pulley. A force of 1oN is applied to the other end, what is the acceleration of the mass? What is the angular acceleration of the pulley?