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# Physics Write Up: The Spin Top

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### Physics Write Up: The Spin Top

1. 1. III-RubidiumGroup 3 SPINNING TOPLeader: Jessica Kabigting – researcher, write-up, explanationMembers: 1. Renz Baluyot - actor 2. Deo Bengo – actor 3. Jovi Cruz - actor 4. Patrick Elegado – explanation, actor 5. Justin Morales – researcher, scriptwriter 6. Bea dela Pena - actor 7. Charlotte Gallardo - actor 8. Hazel Dumo – actorBrief Introduction: Spinning tops have been around so long that no one knows who spun the first one. Fromall corners of the globe have various tops been introduced—the tsa lin of China, the Diabolo ofEurope and Japan’s koma asobi. Some tops are plunger tops, which spin when the plunger is pumped up and down, whileothers are finger tops, which spin by twirling between the thumb and other fingers. There arealso flip tops, whip tops, which are spun by hitting with a lash and the “common” peg top, whichis spun by winding a string or cord around the top and then throwing the top to unwind thestring. These tops differ in size, shape, material and many other aspects, like the method ofrelease, as mentioned above. These factors greatly affect or help determine the motion of thetop. (However, for this presentation, we will be using Beyblades, which are modified tops.)Discussion: a) Physics Concepts (Theoretical Explanation) a. The Perfect Top - is acorn-shaped (broad and rounded at the top, narrowing to a point at the bottom) - has a principal rotation axis that goes through its center of mass (center of gravity / balance point of the object)
2. 2. - is released on a frictionless surface - is perfectly balanced and weighted - If there was a perfect top, it would spin almost indefinitely provided no external torque would be applied to it. Fig. 1. The “Perfect” Top with an acorn-like shape and an especially narrow point for minimal contact with the supposedly frictionless surfaceb. The Top at Rest - possesses potential/stored energy - has no movement until acted upon by an external forcec. The Top in Motion - Torque  the force exerted via snapping/string, etc. (depending on how the top is released or set into motion)  must be applied perpendicular the top’s radius - Potential energy is changed to kinetic energy. - The spinning top rotates around an unseen principal axis (See Fig.2), which is a symmetry axis of the top. (Note: For each unique symmetry axis, the Fig. 2. The principal object has a moment of inertia value that spin/symmetry axis (the black determines how it will spin when a torque is line) is where the center of mass applied.) of the top must be for ideal circular motion. - Initially spins in vertical fashion (the top’s fastest and most stable spin) - Precession Torque = spin angular momentum - produces change in L that is perpendicular to L (change in direction ≠ change in size) - Circular motion: precession -> mismatch between spin axis and center of massd. The Top Slowing Down
3. 3. - Precession (the effect of gravity  causes wobbling) i. Mismatch/misalignment of spin/principal axis and the center of mass ii. Wobbling = leaning away from up and down axis iii. Causes a loss of velocity and momentum iv. Makes the top create widening circles as it spins slower, until it eventually falls v. In a direction determined by the torque exerted by weight - Friction created between top’s tip and floor also slows down the top’s motion/ contributes to loss of velocity. Fig. 3. Precession is the deviation of the top from the principal spin axis. The torque exerted by the top’s weight determines it. e. Factors / Trends that Affect the Movement of the Top ↑ Magnitude of Release = ↑ Force applied = ↑Torque ↑ Balance (equal distribution of weight/shape)= ↑ spin time ↑ Surface area of bottom = ↑ Contact with floor = ↑friction = ↓ spin time ↓ Radius = ↑ speed (like figure skater) ↑ mass = ↑ weight = ↑ wobblingb) Mathematical Explanation
4. 4. Fig. 4. Shows the derivation of omega (precession) for the top, withrelated quantities such as angular momentum, torque, time, radius (lever arm), weight and angular displacement