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A sphere of mass 50gm and radius 10cm rolls without slipping with a velocity of 5cm/s.
Its total kinetic energy in ergs is?
 2 years ago
 2 years ago
A sphere of mass 50gm and radius 10cm rolls without slipping with a velocity of 5cm/s. Its total kinetic energy in ergs is?
 2 years ago
 2 years ago

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stanBest ResponseYou've already chosen the best response.1
For rolling w/o slipping, and choosing teh cm of the cm of teh sphere as the rotation point, \[K _{total}=K _{transl}+K _{rot}=1/2mv^{2}+1/2I \omega ^{2} = 1/2mv^{2}+1/2(2/5mr ^{2})(v/r)^{2}=7/10 mv^{2}\] You can also choose the point of contact as the rotation point and use teh parallel axis theorem to get the same answer
 2 years ago

stanBest ResponseYou've already chosen the best response.1
Choose the point of contact as the rotation point... thus the point of rotation has been moved a distance r from the center of mass of the sphere. Parallel axis theorem says \[I _{\parallel} = I _{cm} + mr ^{2}\] where, again, r is the distance the point of rotation has been displaced from the center of mass (cm) of the sphere. Now, all energy is rotational: \[K _{total} = K _{rot} = 1/2 I _{\parallel} \omega ^{2} \] \[= 1/2 (2/5 mr ^{2} + mr ^{2})*(v/r)^{2}\] \[=1/2(7/5 mr ^{2})*(v ^{2}/r ^{2}) = 7/10 mv ^{2}\]
 2 years ago

ac7qzBest ResponseYou've already chosen the best response.0
You have a combination of linear and rotational KE. These guys are telling you true. P.S. Who uses ergs any more? I haven't heard the term since 1950s scifi.
 2 years ago
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