Learning It is generally a idea to gain an understanding of the \"size of units.

Question

Learning It is generally a idea to gain an understanding of the "size of units. Either below and calculate ng your results to the nearast power of 10, categorize each of the sports balls according to the order of magnitude of the some of the balls are hollow) X 10-5 kg.rr? 10-4 kg. m2 10-3 kg-- 10-2 kg i 2.1T'kg me -.-.1kg. ? golf ball tennis ball As a physics demonstration, you want a special bowling ball made to demonstrate exactly 1 kg m2, so that r students can rotate the ball about its center of mass to get a "feer" for how "big 1 kg m2 is. The bowling Is most familiar to your students has a weight of 15.2 pounds and have a circumference of 26.6 inches, but do not have a moment-of-inertia equal to 1 kg m2 Since the sporting goods manufacturer has no understanding of how "big" 1 kg m2 is, calculate the diameter of the demo bowling ball (in inches) it will need to manufacture. Assume that bowling balls are solid, with a constant density 16.98 in

Explanation / Answer

The equation for moment of inertia for a sphere is I= 2/5mR2

where m = mass and R = radius

Using the data given for a standard bowling ball (15.2 lb = 26.6 in circumference) lets do some unit conversions to find the density in kg/m^3

15.2 lb x 1 kg/2.2lb = 6.91 kg

26.6 in x 2.54 cm/in x 1 m/ 100 cm = 0.676 m in circum. = 2R => R = 0.107 m

V= 4/3R3 = 4/3(0.107 m)3 = 0.00521 m3

Density = 6.91 kg/0.00521 m3 = 1326.73 kg/m3

So, Density = = m/V

rearranging that m=*V

plugging into moment of inertia equation: I = 2/5(*V*R2) = 2/5(*4/3*R3*R2)

Now to solve for R when I = 1 kg m2

1 kg m2 = 2/5(1326.73 kg/m3*4/3*R3*R2)

Radius = R = 0.214 m = 8.425 in

Diameter = 2R = 16.85 inches! Thats a big bowling ball!

Calculation may get wrong (chances are very low BTW) but procedure is 200% correct.

Please rate my answer if you find it helpful, good luck...

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

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