<< Chapter < Page Chapter >> Page >
Rolling motion is equivalent to pure rotation about the axis at the point of contact, which is parallel to central axis.

The pure rolling is a combination of pure rotation and translation. Obviously, it can not be termed as pure rotation as far as the actual motion is concerned. We can, however, exploit the fact that the disk in rolling is actually rotating at any given instant - not over a period but for an instant. This enables us with a very powerful alternative technique to analyze rolling motion.

The alternative consideration assumes rotation about an axis passing through the point of contact and perpendicular to the plane of rotating disk. Each particle can be considered to rotate about the axis instantaneously i.e. at a particular instant. Clearly, this is an equivalent analysis paradigm that gives the same result as when rolling motion is considered as combination of rotation and translation.

Rolling motion as pure rotation

Each particle of the body can be considered to rotate about the axis through the contact point with same angular velocity.

Under this alternative analysis framework, the angular velocities of all particles about this instantaneously stationary axis are considered same. Importantly, this unique angular velocity is equal to angular velocity of rolling (ω). Depending on the linear distance of the particles from the contact point, their linear velocity vary. This alternative framework is consistent with the fact that linear velocities of the particles away from the point of contact are indeed greater as worked out in previous module titled " Rolling motion ".

Rolling motion as pure rotation

The particles of the body away from the contact point moves with increasing speed.

Equivalence of pure rolling

The most important aspect of the equivalence of analysis frameworks, as described earlier, is that rolling motion, which is a combination of pure translation and rotation in physical sense, is described in terms of pure rotation only for the analysis of the motion. In this analysis, we do not need to consider translation at all, as if the rolling body were stationary.

In the nutshell, the equivalent description of rolling in terms of pure rolling has following important considerations :

1. The axis of rotation through contact point is parallel to central axis. This axis is instantaneously at rest and is also referred as "Instantaneous axis of rotation (IAOR)"

2. Each particle of the body is rotating about IAOR with an angular velocity given by :

ω = v C R

where " v C " is the linear velocity of center of mass and "R" is the radius of the disk.

3. The linear velocity of any of the position within the rotating disk is obtained by using the relation,

v = ω x r

The vector notation of the relation above is important. It emphasizes that the linear velocity is directed such that it is perpendicular to both angular velocity vector ( ω ) and position vector ( r ). In the figure below, the vector ω is into the plane of figure i.e. angular velocity vector is perpendicular to xy-plane. The velocity vector being perpendicular to angular velocity vector, therefore, lies in xy-plane. Further, the velocity vector is perpendicular to the positions vector drawn from the point of contact. Note that this is the requirement of pure rotation. The linear velocity should be tangential to the circular path of the particle about the axis in pure rotation.

Questions & Answers

I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask