A simple piece of apparatus to aid the understanding of the relationship between angular velocity and linear velocity

Vertical circular motion is a widely used example to explain non-uniform circular motion in most undergraduate general physics textbooks. However, most of these textbooks do not elaborate on the case when this motion turns into projectile motion under certain conditions. In this paper, we describe thoroughly when a mass attached to a cord, moving in a vertical circular motion, turns into a projectile and its location and velocity when it rejoins the circular orbit. This paper provides an intuitive understanding, supported by basic kinematic equations, to give an interesting elegant connection between circular motion and projectile motion—something lacking in most physics textbooks—and will be very useful to present to an undergraduate class to deepen their understanding of both models of motion.

Section: Introductionmentioning

confidence: 99%

Projectile motion of a once rotating object: physical quantities at the point of return

Arabasi¹

2016

“…Their rotational counterparts, angular velocity ( ω) and angular acceleration ( α) however remain relatively unexplored. There have been limited studies on ω and α in the context of rigid bodies, rolling motion and uniform circular motion [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

An inventory on rotational kinematics of a particle: unravelling misconceptions and pitfalls in reasoning

Mashood

Singh

2012

Student difficulties regarding the angular velocity () and angular acceleration () of a particle have remained relatively unexplored in contrast to their linear counterparts. We present an inventory comprising multiple choice questions aimed at probing misconceptions and eliciting ill-suited reasoning patterns. The development of the inventory was based on interactions with students, teachers and experts. We report misconceptions, some of which are parallel to those found earlier in linear kinematics. Fixations with inappropriate prototypes were uncovered. Many students and even teachers mistakenly assume that all rotational motion is necessarily circular. A persistent notion that the direction of and should be ‘along’ the motion exists. Instances of indiscriminate usage of equations were identified.

“…When it comes to pedagogical concerns and students' difficulties with rotational kinematics, studies so far have been primarily in the context of rigid bodies and rolling motion [4][5][6][7]. The difficulty in comprehending ω in the case of uniform circular motion was addressed by Unsal [8]. Most studies stress the problems in understanding the relation between angular and linear variables.…”

Section: Introductionmentioning

confidence: 99%

Variation in angular velocity and angular acceleration of a particle in rectilinear motion

Mashood¹,

Singh²

2012

We discuss the angular velocity () and angular acceleration () associated with a particle in rectilinear motion with constant acceleration. The discussion was motivated by an observation that students and even teachers have difficulty in ascribing rotational motion concepts to a particle when the trajectory is a straight line. We present some details of our observations. A formal derivation of ω and α is presented which reveals ‘surprising’ and non-intuitive aspects, namely non-monotonic behaviour with an associated extremum. The special case of constant velocity is studied and we find that angular acceleration associated with it also has an extremum. We discuss a plausible source of difficulty.