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Chapter 11: Problem 24

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 baseball's angular momentum will be obtained from the step 3's calculation, make sure to correctly convert units in step 1 and correctly apply the formulas for moments of inertia and angular momentum in steps 2 and 3 respectively.

Step by step solution

01

Convert units to SI

Firstly, the given units should be converted to SI units. The mass should be converted from grams to kilograms by multiplying by \(0.001\) and the diameter should be converted to radius, in meters, by dividing by \(2\). Also, the radius should be converted to meters by dividing by \(100\). The angular velocity should be converted from rpm to rad/s by multiplying by \(\frac{2\pi}{60}\). Let's calculate these conversions.
02

Compute moment of inertia I for a sphere

Next, calculate the moment of inertia for the baseball using the formula \(I = \frac{2}{5}mr^2\), which is specific for a uniform solid sphere. Substitute the mass and radius already converted into this formula and calculate the moment of inertia.
03

Compute angular momentum L

Finally, the angular momentum \(L\) can be calculated by substituting the previously calculated values for the moment of inertia \(I\) and the angular velocity \(\omega\) into the formula \(L = I \omega\). Calculate the angular momentum to finish.

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Most popular questions from this chapter

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