A uniform disk is attached at the rim to a vertical shaft and is used as a cam.

Question

A uniform disk is attached at the rim to a vertical shaft and is used as a cam. The disk has a diameter of 61 cm and a mass of 140 grams. The shaft rotates uniformly about its axis at 79rpm. Find the kinetic energy of the disk. Sorry cannot supply the drawing.

Here is my method of solving which isn't correct. Please analyze and tell me where I'm going wrong. I know that I need to use the parallel axis theorem, but how to use it is confusing to me.

K = 1/2mv^2 + 1/2 I^2

Idisk = Icom + mh^2 = .5mr^2 * mr^2

= 1/2 (.14kg)(.305m)^2 + .14(.305^2) = 19.535 * 10*-3

Find .   79 rpm * 1/60 sec * 2 = 8.273 rad/sec

Find v = = (.305)(8.273) = 2.52 m/s

so K = .5(.14)(2.52^2) + .5(19.535*10^-3)(8.273^2)= 1.113 J

The correct answer is .67 J What's wrong with my solution. Thanks!!

Explanation / Answer

The mass of the disk m = 0.140kg

the radius of the disk r = 0.61m

The angular velocity = 79 rpm

K = 1/2mv^2 + 1/2 I^2

The moment of inertia of the disk about its axis

Idisk = 0.5mr^2

        = 1/2 (0.14kg)(0.305m)^2

        = 6.5 * 10*-3 kgm^2

Find .   79 rpm * 1/60 sec * 2 = 8.273 rad/sec

Find v = r = (0.305)(8.273) = 2.52 m/s

so K = 0.5(0.14)(2.52^2) + 0.5(6.5*10^-3)(8.273^2)

       = 0.6669J

        = 0.67 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.