ROTATIONAL DYNAMICS. ROTATIONAL DYNAMICS AND MOMENT OF INERTIA  A Force applied to an object can cause it to rotate.  Lets assume the F is applied at.

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Presentation transcript:

ROTATIONAL DYNAMICS

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.

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:

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.

EXAMPLE  Find the moment of inertia for figure A.

 Find the moment of inertia in figure B

Here is a sculpture that consists of three small, heavy spheres attached by very lightweight (massless) 10-cm-long rods as shown in FIGURE 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

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

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?

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

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?