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Chapter 10: Problem 51

For each of the following rotating objects, describe the direction of the angular momentum vector: (a) the minute hand of a clock; (b) the right front tire of a car moving backward; (c) an ice skater spinning clockwise; (d) the earth rotating on its axis.

Short Answer

Expert verified
(a) Into the clock; (b) Into the car; (c) Downward; (d) Away from the North Pole.

Step by step solution

01

Understanding Angular Momentum

Angular momentum is a vector quantity, requiring both magnitude and direction. The direction of the angular momentum vector is determined by the right-hand rule. To use the rule, curl the fingers of your right hand in the direction of rotation, and your thumb will point in the direction of the angular momentum vector.
02

Minute Hand of a Clock

For a clock's minute hand rotating clockwise when viewed from the front (which is typically the cross-sectional view of a clock), use the right-hand rule. Curl your fingers in the clockwise direction. Your thumb points into the plane of the clock, indicating that the angular momentum vector is directed into the clock.
03

Right Front Tire of a Car Moving Backward

If the car is moving backward, the tire appears to rotate clockwise when viewed from the side (driver's perspective). Using the right-hand rule, curl your fingers in the clockwise direction of rotation. Your thumb will point into the car, meaning the angular momentum vector points into the car.
04

Ice Skater Spinning Clockwise

For an ice skater viewed from above, spinning clockwise, apply the right-hand rule. Curl your fingers in the clockwise direction of the spin. Your thumb will point downward towards the ice, indicating the angular momentum vector is directed down.
05

Earth Rotating on Its Axis

Looking at Earth from above the North Pole, it rotates counterclockwise. Applying the right-hand rule, curl your fingers in the counterclockwise direction, and your thumb will point up away from Earth. Hence, Earth's angular momentum vector points away from the North Pole.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Right-hand Rule
The right-hand rule is a simple yet powerful technique for determining the direction of angular momentum. It involves using your right hand to mimic the direction of an object's rotation. Here's how it works:
  • Point your thumb in the direction you wish to find the angular momentum vector.
  • Curl your fingers in the direction of the object's rotation.
  • Your thumb will naturally point in the direction of the angular momentum vector.
For example, if you have a clock's hand rotating clockwise, curl your fingers around the clock face following this direction. Your thumb will point into the plane, signifying the vector pointing into the clock.
Vector Quantity in Physics
In physics, certain quantities are described not just by size or magnitude but also by direction. Angular momentum is one such vector quantity. This means it has both a size (how fast something is spinning) and a direction (which way it points).
  • The direction is essential because it helps determine how objects interact in rotational motion.
  • Direction is often determined using tools like the right-hand rule.
Understanding vector quantities enables us to grasp intricate details about motion, like how different spins and rotations influence each other.
Direction of Rotation
The direction of rotation plays a crucial role in determining the angular momentum direction of a spinning object. By visually observing which way an object spins, we can use the right-hand rule to determine its angular momentum vector.
  • Clockwise rotation, like the minute hand of a clock, typically results in a direction into the surface it's viewed against.
  • Counterclockwise rotation, such as the Earth's rotation from the North Pole, results in a direction away from the surface.
The direction of rotation directly affects how objects behave when they spin, and it helps in predicting future movements and interactions.
Physics Problem Solving
Solving physics problems often involves recognizing patterns and using logical tools, like the right-hand rule, to find solutions.
  • Start by identifying the type of motion and the object's perspective.
  • Use the right-hand rule to establish the direction of vectors involved.
  • Break down the problem step-by-step, considering all vector quantities, like angular momentum.
This methodical approach is crucial in dealing with complex problems involving rotations, ensuring that you incorporate all aspects of vector direction and magnitude. Problem-solving in physics leads to a deeper understanding of how the universe behaves, from simple spinning toys to massive celestial bodies.

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Most popular questions from this chapter

A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of \(18 \mathrm{~kg} \cdot \mathrm{m}^{2}\). She then tucks into a small ball, decreasing this moment of inertia to \(3.6 \mathrm{~kg} \cdot \mathrm{m}^{2}\). While tucked, she makes two complete revolutions in \(1.0 \mathrm{~s}\). If she hadn't tucked at all, how many revolutions would she have made in the \(1.5 \mathrm{~s}\) from board to water?

A solid, uniform cylinder with mass \(8.00 \mathrm{~kg}\) and diameter \(0.20 \mathrm{~m}\) is spinning at \(20 \mathrm{rad} / \mathrm{s}\) on a thin, frictionless axle that passes along the cylinder axis. You bring the cylinder to rest by placing your hand on the rim. What is the friction force between your hand and the cylinder if the cylinder comes to rest in \(5 \mathrm{~s} ?\)

A uniform ladder \(7.0 \mathrm{~m}\) long weighing \(450 \mathrm{~N}\) rests with one end on the ground and the other end against a perfectly smooth vertical wall. The ladder rises at \(60.0^{\circ}\) above the horizontal floor. A \(750 \mathrm{~N}\) painter finds that she can climb \(2.75 \mathrm{~m}\) up the ladder, measured along its length, before it begins to slip. (a) Make a free- body diagram of the ladder. (b) What force does the wall exert on the ladder? (c) Find the friction force and normal force that the floor exerts on the ladder.

You are trying to raise a bicycle wheel of mass \(m\) and radius \(R\) up over a curb of height \(h .\) To do this, you apply a horizontal force \(F\) (Figure 10.82 ). What is the smallest magnitude of the force \(\overrightarrow{\boldsymbol{F}}\) that will succeed in raising the wheel onto the curb when the force is applied (a) at the center of the wheel, and (b) at the top of the wheel? (c) In which case is less force required?

A uniform \(2 \mathrm{~kg}\) solid disk of radius \(R=0.4 \mathrm{~m}\) is free to rotate on a frictionless horizontal axle through its center. The disk is initially at rest, and then a \(10 \mathrm{~g}\) bullet traveling at \(500 \mathrm{~m} / \mathrm{s}\) is fired into it as shown in Figure \(10.59 .\) If the bullet embeds itself in the disk at a vertical distance of \(0.2 \mathrm{~m}\) above the axle, what will be the angular velocity of the disk?
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