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Chapter 11: Problem 18

Express the units of angular momentum (a) using only the fundamental units kilogram, meter, and second; (b) in a form involving newtons; (c) in a form involving joules.

Short Answer

Expert verified
The units of Angular Momentum are: (a) Fundamental Units: kg m虏/s (kilogram meter squared per second); (b) Newtons: Nm (Newton meter); (c) Joules: Angular momentum can technically be expressed as Joules seconds (Js), but is not commonly used or recognized in this form because Joules are primarily associated with energy.

Step by step solution

01

Express in Fundamental Units

As previously defined, the SI unit of Angular Momentum is kg m\(^2\)s\(^{-1}\). Therefore, using only the fundamental units of kilogram, meter, and second, Angular Momentum is expressed as \( L = kg \cdot m^{2} \cdot s^{-1} \).
02

Express in Form Involving Newtons

A Newton (N) is the SI unit for force and it is defined as kgm/s\(^2\). To express Angular Momentum in terms of Newtons, we substitute this definition of a Newton into the expression for Angular Momentum, yielding \( L = N \cdot m \).
03

Express in Form Involving Joules

A Joule (J) is the SI unit for energy and it is defined as Nm. To express Angular Momentum in terms of Joules, one way might be to substitute the definition of Joule into our Newton expression from Step 2. However, this definition doesn't fit elegantly with the concept of Angular Momentum. It's important to note that Joules are primarily used in energy states, not in relation to angular momentum, which is often more closely associated with motion and rotational systems than energy states per se.

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Most popular questions from this chapter

You're choreographing your school's annual ice show. You call for eight \(65-\mathrm{kg}\) skaters to join hands and skate side by side in a line extending \(11 \mathrm{~m}\). The skater at one end is to stop abruptly, so the line will rotate rigidly about that skater. For safety, you don't want the fastest skater to be moving at more than \(9.8 \mathrm{~m} / \mathrm{s}\), and you don't want the force on that skater's hand to exceed \(300 \mathrm{~N}\). What do you determine is the greatest speed the skaters can have before they execute their rotational maneuver?

Example 11.2: A skater has rotational inertia \(5.31 \mathrm{~kg} \cdot \mathrm{m}^{2}\) with his arms outstretched and a baseball glove on each hand; the pocket of each glove is \(123 \mathrm{~cm}\) from his rotation axis. He's spinning with angular velocity pointing upward and with magnitude \(0.950\) rev/s. He catches a \(146-\mathrm{g}\) baseball moving at \(24.7 \mathrm{~m} / \mathrm{s}\) perpendicular to his arms and heading straight toward the pocket of his glove. Find his subsequent spin rate if he catches the ball with (a) his left hand and (b) his right hand.

Jumbo is back! Jumbo is the 4.8-Mg elephant from Example 9.4. This time he's standing at the outer edge of a \(15-\mathrm{Mg}\) turntable of radius \(8.5 \mathrm{~m}\), rotating with angular velocity \(0.15 \mathrm{~s}^{-1}\) on frictionless bearings. Jumbo then walks to the center of the turntable. Treating Jumbo as a point mass and the turntable as a solid disk, find (a) the angular velocity of the turntable once Jumbo reaches the center and (b) the work Jumbo does in walking to the center.

Why is it easier to balance a basketball on your finger if it's spinning?

A force \(\vec{F}=1.3 \hat{\imath}+2.7 \hat{\jmath} \mathrm{N}\) is applied at the point \(x=3.0 \mathrm{~m}, y=0 \mathrm{~m}\). Find the torque about (a) the origin and (b) the point \(x=-1.3 \mathrm{~m}, y=2.4 \mathrm{~m}\).
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