b. At the bottom of the ramp, find the ratio of the object's rotational kinetic energy to its translational kineticenergy-NatNran In arder for an object to rull smoothly (with constant angular acceleration) down a ramp, it must have either spherical orcylindrical symmetry. Consider spherically and cylindrically symmatric objects with mas Mand cuter radius Rrollingwithout slipping down an incline of height h and angle e from the horizcntal. The rotational inertias of such objects canbe writtem in the genralised form: /- cMR", uhere cis a shape factor whose valar depends cn the gecmetry of theobject. (f you look at thr lable of rotational inertias in ther testhook you'l br able to se that this is truc.)(For this questin, cnider M. R., 0, md gan the givn quantities-espres your aners in ler of eal of these quantities. Sinplijy yoar ansra a ack an you can.)If the object starts from rest at the very top of the ramp before rolling freely downthe ramp without slipping, find the object's (linear) rotational speed at the botom of theramp. (Hint ase coseroation of energy

Answered: Image /qna-images/answer/61eed72c-d098-4d2a-9022-befb42938f7b.jpg

In onder for an oject to oll smoothly (with comtant angular acceleration) downaramp, itust have either spherical or cylindrical symmetry. Consider spherically and cylindrically symmetric objects with ma M and outer radius R rolling without slipping dowman incline of height h and angle eom the horinontal. The rotational inertian of sach objects cam beweritm in the gemeralined foem: I- M", where cisashape factor whoe valar dependa on the geometry of the object. Fyu lk at the tabie of netatimal inerti in the teahek yeubrale te e that this in tra Fr this qurstim, mider M.R md ga the gi quntti-pr yr amm in r of me al ef thee quntitin. Simpliy your a maka you cm.) lf the object starts from st at the very top of the ramp befone nolling frdy down the ramp witheut slipping, find the object's (lineur) rotational speed at the botom of the zamp. Hint: ae ameratim of emergy

In onder for an oject to oll smoothly (with comtant angular acceleration) downaramp, itust have either spherical or cylindrical symmetry. Consider spherically and cylindrically symmetric objects with ma M and outer radius R rolling without slipping dowman incline of height h and angle eom the horinontal. The rotational inertian of sach objects cam beweritm in the gemeralined foem: I- M", where cisashape factor whoe valar dependa on the geometry of the object. Fyu lk at the tabie of netatimal inerti in the teahek yeubrale te e that this in tra Fr this qurstim, mider M.R md ga the gi quntti-pr yr amm in r of me al ef thee quntitin. Simpliy your a maka you cm.) lf the object starts from st at the very top of the ramp befone nolling frdy down the ramp witheut slipping, find the object's (lineur) rotational speed at the botom of the zamp. Hint: ae ameratim of emergy

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

b. At the bottom of the ramp, find the ratio of the object's rotational kinetic energy to its translational kinetic
energy-
Nat
Nran

In arder for an object to rull smoothly (with constant angular acceleration) down a ramp, it must have either spherical or
cylindrical symmetry. Consider spherically and cylindrically symmatric objects with mas Mand cuter radius Rrolling
without slipping down an incline of height h and angle e from the horizcntal. The rotational inertias of such objects can
be writtem in the genralised form: /- cMR", uhere cis a shape factor whose valar depends cn the gecmetry of the
object. (f you look at thr lable of rotational inertias in ther testhook you'l br able to se that this is truc.)
(For this questin, cnider M. R., 0, md gan the givn quantities-espres your aners in ler of e
al of these quantities. Sinplijy yoar ansra a ack an you can.)
If the object starts from rest at the very top of the ramp before rolling freely down
the ramp without slipping, find the object's (linear) rotational speed at the botom of the
ramp. (Hint ase coseroation of energy

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