Abstract
You know how to describe the rotation of a wheel around a fixed or moving axis, using the angle, the angular velocity, and the angular acceleration of the wheel. And you know how to find the kinetic energy of a rotating rigid body. But what causes changes in rotational motion? For translational motion we can use Newton’s second law to determine the change in the translational state, in the translational momentum, from the external forces acting on a body. We use this both to find the acceleration of a body, and from the acceleration we can calculate the motion, and to find conservation laws for the translational momentum. Can we find a similar law for rotational motion? In this chapter we will introduce the rotational analogue to translational momentum: rotational momentum or angular momentum; the rotational analogue to force: torque; and the rotational analogue to Newton’s second law: Newton’s second law for rotational motion. Armed with these tools you will see that you are ready to solve any problem of moving and rotating rigid bodies, such as figuring out what causes a ball to spin or how you jump-spin on skates.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Notice that the torque \(\mathbf {\tau }\) points in the z-direction, which is also the direction of the rotation vector, \(\mathbf {\omega } = \omega \, \mathbf {k}\). This suggests a vector formulation of Newton’s second law for rotational motion: \(\sum \mathbf {\tau }_{j} = I \mathbf {\alpha }\). Unfortunately, this is generally not correct. We will return to a vector formulation later.
- 2.
Notice that O must be a point on the rotation axis.
- 3.
You can learn more about this process, and look at how aggregate flakes look in the PhD thesis of Christopher David Westbrook at (http://www.met.rdg.ac.uk/sws04cdw/thesis.pdf).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Malthe-Sorenssen, A. (2015). Dynamics of Rigid Bodies. In: Elementary Mechanics Using Matlab. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-19587-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-19587-2_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19586-5
Online ISBN: 978-3-319-19587-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)