Many machines employ cams for various purposes, such as opening and closing valv
ID: 1607387 • Letter: M
Question
Many machines employ cams for various purposes, such as opening and closing valves. The cam is a circular disk rotating on a shaft that does not pass through the center of the disk. In the manufacture of the cam, a uniform solid cylinder of radius R is first machined. Then an off-center hole of radius R/2 is drilled, parallel to the axis of the cylinder, and centered at a point a distance R/2 from the center of the cylinder. The cam, of mass M, is then slipped onto the circular shaft and welded into place. What is the kinetic energy of the cam when it is rotating with angular speed about the axis of the shaft? (Use omega for , M, and R as appropriate in your equation.) K = 13/24*MR^2w^2 Click here to preview your answer. Incorrect: Your answer is incorrect. Click here for help with symbolic formatting.
The K=13/24*MR^2w^2 was my answer i got but I submitted that and it was not correct can someone please clarify
Explanation / Answer
Mass of original cylinder,
Mo - Mo/4 = M
M = 3Mo / 4
moment of inertia of original cylinder from parallel axis theorem,
lcm + Mo*(R / 2)^2 = MoR^2 / 2 + MoR^2 / 4
l' = 3MoR^2 / 4
MOI of hole,
l'' = 1/2 * (mo/4) * (R/2)^2
l'' = MoR^2 / 32
MOI of whole system,
l = l' - l''
l = MoR^2 / 4 - MoR^2 / 32
l = (23 / 32)*MoR^2 = (23 / 32) * 4MR^2 / 3
l = 23MR^2 / 24
KInetic energy of cam,
KE = (1/2)*l*w^2
KE = 23M* R^2*w^2 / 48
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