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Chapter 11: Problem 26

A 7.4 -cm-diameter baseball has mass \(145 \mathrm{g}\) and is spinning at 2000 rpm. Treating the baseball as a uniform solid sphere, what's its angular momentum?

Short Answer

Expert verified
The angular momentum of the spinning baseball is \( 0.00779 \) kg m虏/s.

Step by step solution

01

Convert from diameter to radius and from g to kg

First, the radius of the baseball needs to be found by halving the diameter. The given diameter is 7.4 cm, so the radius is \( r = \frac{7.4}{2} = 3.7 \) cm or \( 0.037 \) m. The mass is also given as 145g, we need convert it to kg, which is \( m = \frac{145}{1000} = 0.145 \) kg.
02

Convert the angular speed from rpm to rad/s

Next, convert the angular speed from rpm (revolutions per minute) to rad/s (radians per second). \( \omega = 2000 \times \frac{2 \pi}{60} = 209.44 \) rad/s.
03

Calculate the moment of inertia

Now calculate the moment of inertia of the solid sphere using the formula \( I = \frac{2}{5} m r^2 \). Substituting the known values gives \( I = \frac{2}{5} \times 0.145 \times (0.037)^2 = 0.0000372 \) kg m虏.
04

Calculate the angular momentum

Finally, calculate the angular momentum of the solid sphere using the formula \( L = I \omega \). Substituting the known values gives \( L = 0.0000372 \times 209.44 = 0.00779 \) kg m虏/s.

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