Chapter 1: Q37E (page 331)

Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. The clock hand has a length of $15.0 cm$ and a mass of $6.00 g$ . Take the second hand to be a slender rod rotating with constant angular velocity about one end.

Short Answer

Expert verified

Hence, the angular momentum is $4.71 \times 10^{- 6} {kgm}^{2} /s$ .

Step by step solution

Definition of angular momentum of second hand of a clock

The magnitude of angular momentum of second hand of a clock about an axis through the center of the clock face (a symmetry axis) is found using,

$L = I ω$

Where, $I$ is moment of inertia of rod rotating about an axis through one end ie, $I = \frac{1}{3} m l^{2}$

Then, the angular momentum is written as:

$L = \frac{1}{3} m l^{2} ω$

Evaluate the angular momentum

Since, second hand makes a complete revolution each $60$ seconds, its angular speed is:

$ω = \frac{1 r e v}{60 s} = \frac{2 π r a d}{60 s}$

The angular momentum is calculated as follows:

$L = \frac{1}{3} m l^{2} ω = \frac{1}{3} m l^{2} (\frac{2 π r a d}{60 s}) = \frac{1}{3} \times 6 \times 10^{- 3} \times {(0.150)}^{2} (\frac{2 π r a d}{60 s}) = 4.71 \times 10^{- 6} {kgm}^{2} /s$

Thus, the angular momentum is $4.71 \times 10^{- 6} {kgm}^{2} /s$ .

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Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. The clock hand has a length of $15.0 cm$ and a mass of $6.00 g$ . Take the second hand to be a slender rod rotating with constant angular velocity about one end.

Short Answer

Step by step solution

Definition of angular momentum of second hand of a clock

Evaluate the angular momentum

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Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. The clock hand has a length of 15.0cmand a mass of 6.00g. Take the second hand to be a slender rod rotating with constant angular velocity about one end.

Short Answer

Step by step solution

Definition of angular momentum of second hand of a clock

Evaluate the angular momentum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Waves Physics

Fields in Physics

Scientific Method Physics

Electricity and Magnetism

Classical Mechanics

Study anywhere. Anytime. Across all devices.

Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. The clock hand has a length of $15.0 cm$ and a mass of $6.00 g$ . Take the second hand to be a slender rod rotating with constant angular velocity about one end.