Spinning Toy Experiment: Physics Principles, Analysis, and Report

This report delves into the physics of a spinning toy experiment, likening the system to a winch with a rotating drum. It examines the change in angular momentum, the torque applied (due to the string pull and the toy's weight), and the centrifugal force generated. The analysis aligns with classical physics, covering Newtonian laws, inertia effects, and the relationship between angular momentum and applied torque. The report outlines potential tests involving different toy diameters, rope materials, speeds, and torque variations, and presents a standardized equation to determine output parameters like spinning speed and generated force. Key equations for angular momentum, torque, and centrifugal force are provided. The conclusion emphasizes the system's adherence to fundamental physics laws and the potential for further exploration through varying physical variables. References to sources on angular momentum, spinning tops, Newton's laws, and industrial separation are included.

The Spinning Toy Experiment
The theory
The scenario can be likened to a winch system in which there is a rope unwinding on a rotating
drum. As the drum rotates, there is a change in angular momentum which maintains the
unwinding. However, in this case, the reverse is what actually happens. The spinning top is to
be excited to spin by pulling the string connected at the centre. The spinning top therefore has
angular momentum which is changing at a rate proportional to the applied torque (pulling the
string). The torque applied is partly due to the weight of the spinning top. Additionally, the
spinning action generates a centrifugal force which must balance with the tangential force
component otherwise the top may either ‘collapse into the circle’ or’ fly off the circle’.
The above can be explained in classical Physics as well. Firstly, the system is in perfect
agreement with all the three fundamental Newtonian laws. Initially, the object was unmoved
hence momentum was zero (neglecting events just before this event); on pulling the string,
there was a change in momentum occurring in the direction of applied torque hence rate of
change in angular momentum is directly proportional to the applied torque (Lumen learning).
To further maintain the spinning action, torque would be applied periodically. As the spinning
action ensues, the inertia effects are encountered by the system and there must be a system
balance to maintain the action (Manchester).
Common example worth noting is in the industrial separation of cream from whole milk. There
is a centrifuge such that as the milk spins, due to centrifugal force, lighter material are thrown
further while dense material (cream) settle at the centre and is therefore skimmed off
(Uoguelph).
In order to ascertain the performance, a number of tests can be done; for example, for different
diameters of the spinning top, different rope materials (paper, plastic, wood etc), altering the
speed and torque. For this case, we can derive a standardized equation to determine the
output parameters such as: speed of spinning, N (revolutions per minute) and the force
generated.
Figure 1: The Spinning action about the vertical axis

The Equation
The initial angular momentum= Lo
Angular momentum during spinning= L= I.w
Therefore dφ= dL/L= Mgrdt/I.w
The speed in rpm therefore becomes: N= Mgr/I.w or 0.5Mgd/I.w
The force generated:
From torque equation: T= MgSin φ x r
However, since this is centripetal force, F= M.a where a=centrifugal acceleration given by a=
V2/r= w2r
Hence F=Mw2r
Let us note that : w= angular speed of the toy, M=mass of the toy, g= gravity (mostly 9.81), d=
diameter of the circle, I= moment of inertia given as 0.5mr2, L= angular momentum,
Figure 2: The force Generated acting towards the centre
Conclusion
To establish the true performance characteristics of the above system, a number of physical
variables can be assigned as mentioned above; For example, the nature of rope used; or varying
the speed of rotation. Besides, the above formulae have revealed that the system is a pure
phenomenon of classical Physics as it obeys all the fundamental laws of physics (Smith).

REFERENCES
Lumen Learning. Conservation of Angular Momentum. 2019. Available at: www. Courses.
Lumenlearning.com/boundless-physics/chapter/conservation-of-angular-momentum/
Manchester. Spinning Tops. 2019. Available at:
www.ypu.manchester.ac.uk/challenges/spinning-tops
Smith, John. Newton’s Three Laws of Motion. Center for Computer Research and Music and
Acoustics. Standford University, 2019. Available at:
www.ccrma.standford.edu/~jos/pasp/Newton_s_Three_Laws_Motion.html
Uoguelph. Clarification and Separation, 2019. Available at:
www.uoguelph.ca/foodscience/book/exporthtml/1906