Peoples Physics Concepts

9.4 Newton’s Second Law for Rotation

9.4 Newton’s Second Law for Rotation

• Apply Newton’s 2nd law in the case of rotational dynamics.

Students will learn to apply Newton’s 2nd law in the case of rotational dynamics.

Key Equations

α=τnet/I

Angular accelerations are produced by net torques,with inertia opposing acceleration; becauseαis the rotational

version of a, linear acceleration,τis the rotational version of F, force, and I is the rotational version of mass.

This is the rotational analog of Newton’s 2nd lawa=Fnet/m

τnet=Στi=Iα

The net torque is the vector sum of all the torques acting on the object. When adding torques it is necessary to

subtract CW from CCW torques.

Guidance

• Use this law just as you did in the Newton’s Laws lessons. First choose a pivot point to takealltorques around,
  and then add up all the torques acting on an object and that will equal the moment of inertia multiplied by the
  angular acceleration.


• Torquesproduce angular accelerations, but just as masses resist acceleration (due to inertia), there is an
  inertia that opposes angular acceleration. The measure of this inertial resistance depends on the mass, but
  more importantly on the distribution of the mass in a given object.Themoment of inertia,I,is the rotational
  version of mass. Values for the moment of inertia of common objects are given above. Torques have only
  two directions: those that produce clockwise (CW) and those that produce counterclockwise (CCW) rotations.
  The angular acceleration or change inωwould be in the direction of the torque.


• Many separate torques can be applied to an object. The angular acceleration produced isα=τnet/I

Example 1

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/413