Question 1

A person is sitting at rest on a stool that is free to rotate about a vertical axis. The person holds in one hand a bicycle wheel that spins rapidly counterclockwise (when viewed from above). The person then stops the wheel with the other hand. What happens as a result?

Accepted Answer

When the person stops the spinning wheel, the angular momentum of the wheel is transferred to the person and stool system, causing them to rotate counterclockwise to conserve angular momentum.

Question 2

A person is sitting at rest on a stool that is free to rotate about a vertical axis. The person holds a bicycle wheel that is rapidly spinning counterclockwise when viewed from above. The person then flips the wheel over. What happens as a result?

Accepted Answer

The answer of A person is sitting at rest on...

Question 3

Suppose you are looking down on a disk that is spinning counterclockwise. If we apply an upward torque to the disk, its angular speed

Accepted Answer

An upward torque applied to a disk spinning counterclockwise will increase its angular speed because torque causes an increase in angular acceleration in the direction of the applied torque.

Question 4

If global warming proceeds during the next century as anticipated, the polar ice caps may melt, substantially raising sea levels around the world (and flooding coastal cities such as New York and New Orleans). What effect will this have on the duration of the day?

Accepted Answer

The melting of polar ice caps and the resulting redistribution of mass closer to the equator due to rising sea levels would increase the Earth's moment of inertia. According to the conservation of angular momentum, this would slow down the Earth's rotation, thereby slightly lengthening the day.

Question 5

When I was a teenager, I saw a Candid Camera sequence in which they filmed a person struggling with a suitcase that (unknown to that person) contained a large and rapidly spinning gyroscope. Imagine you are carrying such a suitcase where the gyroscope's angular velocity is oriented horizontally to your right as you carry it in your right hand. Imagine you try to make a left turn, thus turning the suitcase to the left around a vertical axis. What does the suitcase do?

Accepted Answer

The suitcase tries to rotate around a horizontal axis, with its right face turning upward due to the gyroscopic precession. When you attempt to turn the suitcase to the left, the gyroscope inside resists changes in its plane of rotation, causing a perpendicular reaction force that makes the right side of the suitcase lift.

Question 6

(Challenging!) Experienced players can throw a Frisbee so it skips off the ground (the Frisbee's front edge actually tips upward after the Frisbee hits, enabling it to climb back into the air). If a right-handed player throws a Frisbee in the usual way, it rotates counterclockwise when viewed from above. To skip the Frisbee, which edge has to hit the ground (as seen by the thrower)? (Hint: The Frisbee's angular momentum vector, and thus its rotation axis, changes in the direction of the external torque that the strike applies to the Frisbee.)

Accepted Answer

The answer of (Challenging!) Experienced players can throw a Frisbee...

Question 7

The lengths of the hour and minute hands of a clock are $4 \mathrm{~cm}$ and $6 \mathrm{~cm}$, respectively. If the vectors $\vec{u}$ and $\vec{w}$ represent the hour and minute hands, respectively, then $\vec{u} \times \vec{w}$ at 5:00 pm is closest to

Accepted Answer

The answer of The lengths of the hour and minute...

Question 8

The basic SI units of angular momentum are:

Accepted Answer

Angular momentum is defined as the product of the moment of inertia and angular velocity. The moment of inertia has units of $\mathrm{kg} \cdot \mathrm{m}^{2}$, and angular velocity has units of $\mathrm{rad} / \mathrm{s}$ (where radians are dimensionless), resulting in units of $\mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}$ for angular momentum.

Question 9

Suppose you are standing due east of a car traveling southwest. What is the direction of the car's angular momentum around you? Choose from the possible directions below (as seen by a person hovering over you), where A is north, C is east, and so on. If you are using the letters on the book's back cover, you can indicate a double letter by pointing to the letter with two fingers.

Accepted Answer

The answer of Suppose you are standing due east of...

Question 10

Suppose a jet is cruising at a constant velocity due east. At the instant the jet is above your head, what is the direction of the jet's angular momentum around you? Choose from the possible directions presented in problem C7T.3, remembering that this is a top view, with A corresponding to north, C to east, and so on.

Accepted Answer

The answer of Suppose a jet is cruising at a...

Question 11

A friend is running clockwise at a constant speed on a circular track. At the instant your friend is running due east, your friend is due west of you. What is the direction of your friend's angular momentum around you at that instant? Choose from the possible directions presented in problem C7T.3, remembering that this is a top view, with $\mathrm{A}$ corresponding to north, $\mathrm{C}$ to east, and so on.

Accepted Answer

The answer of A friend is running clockwise at a...

Question 12

Suppose that $\vec{u}$ and $\vec{w}$ both have nonzero $y$ and $z$ components, but both also have zero $x$ components. Which components of $\vec{q}=\vec{u} \times \vec{w}$ are nonzero? Select or indicate all the letters that apply.

Accepted Answer

The answer of Suppose that $\vec{u}$ and $\vec{w}$ both have...

Question 13

The set of particles shown below all have the same mass and speed. Which has the largest magnitude of angular momentum around the point $O$ ?

Accepted Answer

The answer of The set of particles shown below all...

Question 14

Four people are sitting at the lettered positions on the rim of a merry-go-round shown below that is slowly turning clockwise. You throw a fairly massive ball horizontally to one of these people, who catches it. To which person should you throw the ball so that catching it most effectively increases the merry-go-round's rotation rate?

Accepted Answer

The answer of Four people are sitting at the lettered...

Question 15

The angular momentum of a particle can be nonzero even if it moves in a straight line

Accepted Answer

Angular momentum is given by $\vec{L} = \vec{r} \times \vec{p}$, where $\vec{r}$ is the position vector of the particle relative to a chosen origin, and $\vec{p}$ is its linear momentum. Even if a particle moves in a straight line, as long as its path is not directly towards or away from the chosen origin (i.e., $\vec{r}$ and $\vec{p}$ are not collinear), the cross product $\vec{r} \times \vec{p}$ will be nonzero, resulting in a nonzero angular momentum.

Question 16

The angular momentum (around a rotating rigid object's center of mass) of an arbitrary particle in that object points directly along the object's rotation axis

Accepted Answer

The angular momentum of a particle in a rotating object is not necessarily aligned with the rotation axis; it depends on the particle's position and velocity relative to the axis.

Question 17

(Tricky!) A bowling ball rolls on the floor at a constant velocity away from you. What is the approximate direction of the ball's total angular momentum around your head? (Hint: How fast do the ball's particles move about the ball's center of mass compared to the speed of the ball's center of mass as it moves away from you? Think about it.)

Accepted Answer

The answer of (Tricky!) A bowling ball rolls on the...

Question 18

(Tricky!) Suppose that a batter hits a foul ball almost exactly vertically in the air. As the ball rises, the magnitude of the torque that the gravitational interaction exerts on the ball around the pitcher:

Accepted Answer

The torque ($\tau$) caused by gravity on the ball around a point (like the pitcher's mound) is given by $\tau = r \times F$, where $r$ is the distance from the point to the line of action of the force (in this case, the weight of the ball), and $F$ is the magnitude of the force (the weight of the ball, which is constant as it depends on mass and gravitational acceleration). As the ball rises vertically, the distance $r$ (horizontal distance to the pitcher) does not change, and neither does the force of gravity acting on the ball. Therefore, the torque remains roughly constant.

Question 19

Which has the larger kinetic energy, a 50-kg person running at a speed of $2 \mathrm{~m} / \mathrm{s}$, or a $5-\mathrm{g}$ nickel falling at a speed of $200 \mathrm{~m} / \mathrm{s}$ ?

Accepted Answer

The answer of Which has the larger kinetic energy, a...

Question 20

A person throws three rocks off a cliff of height $h$ at exactly the same speed $\left|\vec{v}_{i}\right|$, each time, but throwing rock $A$ almost vertically upward, rock $B$ horizontally, and rock $C$ almost vertically downward (see the diagram below).

Which rock hits the ground with the greatest speed? (Ignore air friction.)

Accepted Answer

The answer of A person throws three rocks off a...

Quiz 1: Conservation Laws Constrain Interactions

A person is sitting at rest on a stool that is free to rotate about a vertical axis. The person holds in one hand a bicycle wheel that spins rapidly counterclockwise (when viewed from above) . The person then stops the wheel with the other hand. What happens as a result?

A person is sitting at rest on a stool that is free to rotate about a vertical axis. The person holds a bicycle wheel that is rapidly spinning counterclockwise when viewed from above. The person then flips the wheel over. What happens as a result?

Suppose you are looking down on a disk that is spinning counterclockwise. If we apply an upward torque to the disk, its angular speed

If global warming proceeds during the next century as anticipated, the polar ice caps may melt, substantially raising sea levels around the world (and flooding coastal cities such as New York and New Orleans) . What effect will this have on the duration of the day?

The lengths of the hour and minute hands of a clock are $4 \mathrm{~cm}$ and $6 \mathrm{~cm}$ , respectively. If the vectors $\vec{u}$ and $\vec{w}$ represent the hour and minute hands, respectively, then $\vec{u} \times \vec{w}$ at 5:00 pm is closest to

The basic SI units of angular momentum are:

Suppose that $\vec{u}$ and $\vec{w}$ both have nonzero $y$ and $z$ components, but both also have zero $x$ components. Which components of $\vec{q}=\vec{u} \times \vec{w}$ are nonzero? Select or indicate all the letters that apply.

The set of particles shown below all have the same mass and speed. Which has the largest magnitude of angular momentum around the point $O$ ?

The angular momentum of a particle can be nonzero even if it moves in a straight line

The angular momentum (around a rotating rigid object's center of mass) of an arbitrary particle in that object points directly along the object's rotation axis

(Tricky!) Suppose that a batter hits a foul ball almost exactly vertically in the air. As the ball rises, the magnitude of the torque that the gravitational interaction exerts on the ball around the pitcher:

Which has the larger kinetic energy, a 50-kg person running at a speed of $2 \mathrm{~m} / \mathrm{s}$ , or a $5-\mathrm{g}$ nickel falling at a speed of $200 \mathrm{~m} / \mathrm{s}$ ?

Quiz 1: Conservation Laws Constrain Interactions

A person is sitting at rest on a stool that is free to rotate about a vertical axis. The person holds in one hand a bicycle wheel that spins rapidly counterclockwise (when viewed from above) . The person then stops the wheel with the other hand. What happens as a result?

A person is sitting at rest on a stool that is free to rotate about a vertical axis. The person holds a bicycle wheel that is rapidly spinning counterclockwise when viewed from above. The person then flips the wheel over. What happens as a result?

Suppose you are looking down on a disk that is spinning counterclockwise. If we apply an upward torque to the disk, its angular speed

If global warming proceeds during the next century as anticipated, the polar ice caps may melt, substantially raising sea levels around the world (and flooding coastal cities such as New York and New Orleans) . What effect will this have on the duration of the day?

The lengths of the hour and minute hands of a clock are 4 cm4 \mathrm{~cm}4 cm and 6 cm6 \mathrm{~cm}6 cm , respectively. If the vectors u⃗\vec{u}u and w⃗\vec{w}w represent the hour and minute hands, respectively, then u⃗×w⃗\vec{u} \times \vec{w}u×w at 5:00 pm is closest to

The basic SI units of angular momentum are:

Suppose that u⃗\vec{u}u and w⃗\vec{w}w both have nonzero yyy and zzz components, but both also have zero xxx components. Which components of q⃗=u⃗×w⃗\vec{q}=\vec{u} \times \vec{w}q​=u×w are nonzero? Select or indicate all the letters that apply.

The set of particles shown below all have the same mass and speed. Which has the largest magnitude of angular momentum around the point OOO ?

The angular momentum of a particle can be nonzero even if it moves in a straight line

The angular momentum (around a rotating rigid object's center of mass) of an arbitrary particle in that object points directly along the object's rotation axis

(Tricky!) Suppose that a batter hits a foul ball almost exactly vertically in the air. As the ball rises, the magnitude of the torque that the gravitational interaction exerts on the ball around the pitcher:

Which has the larger kinetic energy, a 50-kg person running at a speed of 2 m/s2 \mathrm{~m} / \mathrm{s}2 m/s , or a 5−g5-\mathrm{g}5−g nickel falling at a speed of 200 m/s200 \mathrm{~m} / \mathrm{s}200 m/s ?

The lengths of the hour and minute hands of a clock are $4 \mathrm{~cm}$ and $6 \mathrm{~cm}$ , respectively. If the vectors $\vec{u}$ and $\vec{w}$ represent the hour and minute hands, respectively, then $\vec{u} \times \vec{w}$ at 5:00 pm is closest to

Suppose that $\vec{u}$ and $\vec{w}$ both have nonzero $y$ and $z$ components, but both also have zero $x$ components. Which components of $\vec{q}=\vec{u} \times \vec{w}$ are nonzero? Select or indicate all the letters that apply.

The set of particles shown below all have the same mass and speed. Which has the largest magnitude of angular momentum around the point $O$ ?

Which has the larger kinetic energy, a 50-kg person running at a speed of $2 \mathrm{~m} / \mathrm{s}$ , or a $5-\mathrm{g}$ nickel falling at a speed of $200 \mathrm{~m} / \mathrm{s}$ ?