Q: A small 1,500 kg plane is traveling to the right at 50 m/s at a height of 150 m above the ground as shown in the diagram. What is the magnitude of the angular momentum of the plane as measured about point P?

$$L = 9.375 \times 10$$^{6}$$\ \mathrm{kg\cdot m^2$/s}$$

Q: Which vector operation is used to calculate the angular momentum $$\vec{L} of a $$particle about a point?

$$\vec{L} = \vec{r} \times \vec{p}$$

Question 1

A 2.3 kg, 1.0 m wide door is swinging open and rotating at an angular speed of 2.5 rad/s when someone throws a snowball which hits the door perpendicularly and causes it to stop rotating. If the mass of the snowball is 0.32 kg and it hits the door at a distance of 0.75 m from the hinge, how fast was it moving right before hitting the door? (Assume $$I_{door} = \frac{1}{3} M L^2$ for the moment of inertia of the door about its end.)

Accepted Answer

$$v_{i} = 13.9\ \mathrm{m/s}$$

Question 2

Which physical principle is primarily used to solve the problem of the snowball hitting the rotating door and causing it to stop?

Accepted Answer

Conservation of angular momentum

Question 3

A small 1,500 kg plane is traveling to the right at 50 m/s at a height of 150 m above the ground as shown in the diagram. What is the magnitude of the angular momentum of the plane as measured about point P?

Accepted Answer

$$L = 9.375 	imes 10$$^{6}$$\ \mathrm{kg\cdot m^2$/s}$$

Question 4

In the plane problem, what is the direction of the angular momentum vector $$\vec{L} as $$calculated about point P?

Accepted Answer

Into the page

Question 5

A wad of sticky clay with mass $$m = 100\ \mathrm{g}$$ and speed $$v = 20.0\ \mathrm{m/s} is $$fired at a solid cylinder of mass $$M = 1.5\ \mathrm{kg}$$ and radius $$R = 0.15\ \mathrm{m}$$, which is initially at rest and mounted on a fixed horizontal axle. The clay sticks to the side of the cylinder at a distance $$d = 0.10\ \mathrm{m}$$ from the axis. What is the angular speed $$\omega of $$the system just after the clay strikes and sticks?

Accepted Answer

$$\omega = 0.615\ \mathrm{rad/s}$$

Question 6

How much of the initial kinetic energy of the clay-cylinder system was transformed into other forms of energy after the collision?

Accepted Answer

$$\Delta KE = 19.3\ \mathrm{J}$$

Question 7

After the clay sticks to the cylinder and the system rotates, what is the direction of the angular momentum of the system?

Accepted Answer

Into the page

Question 8

A uniform spherical star of radius $$R$$ rotates about a diameter with angular velocity $$\omega. $$The star suddenly collapses to a uniform sphere of radius $$R/2$$ due to internal forces. What is the new angular velocity?

Accepted Answer

$$8\omega$$

Question 9

A particle with mass $$1\ \mathrm{kg}$$ has position vector $$\vec{r} = (3\hat{i} + 2\hat{j})\ \mathrm{m}$$ and momentum vector $$\vec{p} = (2\hat{i} - 4\hat{j})\ \mathrm{kg\cdot m/s}. $$What is the angular momentum $$\vec{L} of $$the particle about the origin?

Accepted Answer

$$\vec{L} = (-14)\hat{k}\ \mathrm{kg\cdot m^2$/s}$$

Question 10

Which of the following best describes why angular momentum is conserved in the clay-cylinder collision?

Accepted Answer

No external torques act on the system during the collision

Question 11

If a rotating object suddenly contracts to half its original radius with no external torque, what happens to its angular velocity?

Accepted Answer

It increases by a factor of 8

Question 12

A door of mass $$M$$ and width $$L$$ rotates about its hinges. What is its moment of inertia about the hinges?

Accepted Answer

$$I = \frac{1}{3} M L^2$

Question 13

A clay wad sticks to a rotating cylinder. Which type of collision does this represent?

Accepted Answer

Perfectly inelastic

Question 14

Which vector operation is used to calculate the angular momentum $$\vec{L} of a $$particle about a point?

Accepted Answer

$$\vec{L} = \vec{r} 	imes \vec{p}$$

Question 15

A plane is flying horizontally at a constant speed. If the reference point is directly below the plane, what is the direction of its angular momentum?

Accepted Answer

Into the page

Question 16

If a snowball hits a rotating door and causes it to stop, what can be said about the total angular momentum of the system (door + snowball) just before and just after the collision?

Accepted Answer

It is conserved

Question 17

A solid cylinder of mass $$M$$ and radius $$R$$ rotates about its axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2} M R^2$

Question 18

Which of the following scenarios would NOT conserve angular momentum?

Accepted Answer

A system with an external torque acting during the event

Angular Momentum and Collisions: Study Notes and Problems

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