Q: Which equation best represents the angular momentum $$\vec{L} of a $$single particle with position vector $$\vec{r}$$ and linear momentum $$\vec{p}$$?

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

Q: Which equation expresses the net torque $$\vec{\tau} as $$the rate of change of angular momentum $$\vec{L}$$?

$$\vec{\tau} = \frac{d\vec{L}}{dt}$$

Q: Which equation represents the second equilibrium condition for static equilibrium of a rigid body?

$$\sum_k \vec{\tau}_k = \vec{0}$$

Q: A mass segment $$\Delta m$$ located at $$\vec{r}_i$$ with velocity $$\vec{v}_i in a $$rotating rigid body has angular momentum $$\vec{L}_i. $$Which formula gives $$\vec{L}_i$$?

$$\vec{L}_i = \vec{r}_i \times \Delta m \vec{v}_i$$

Question 1

Which equation best represents the angular momentum $$\vec{L} of a $$single particle with position vector $$\vec{r}$$ and linear momentum $$\vec{p}$$?

Accepted Answer

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

Question 2

A meteor enters Earth's atmosphere with $$\vec{r} = 25\,	ext{km}\,\hat{i} + 25\,	ext{km}\,\hat{j}$$ and $$\vec{p} = 15.0\,	ext{kg}\,(-2.0\,	ext{km/s}\,\hat{j}). $$What is the direction of its angular momentum relative to the observer at the origin?

Accepted Answer

Perpendicular to the $$xy-$$plane, along the $$+z$$ direction

Question 3

Which equation expresses the net torque $$\vec{	au} as $$the rate of change of angular momentum $$\vec{L}$$?

Accepted Answer

$$\vec{	au} = \frac{d\vec{L}}{dt}$$

Question 4

A rigid body rotates about a fixed axis. Which formula gives its angular momentum $$L$$?

Accepted Answer

$$L = I \omega$$

Question 5

A figure skater pulls in her arms while spinning, decreasing her moment of inertia from $$I to$$ $$I'. If $$her initial angular velocity is $$\omega$$, what is her new angular velocity $$\omega'$$?

Accepted Answer

$$\omega' = \frac{I}{I'} \omega$$

Question 6

Which statement best describes the law of conservation of angular momentum?

Accepted Answer

If the net external torque is zero, the total angular momentum remains constant.

Question 7

A bullet of mass $$m = 2.0\,	ext{g}$$ moving at $$500.0\,	ext{m/s}$$ embeds in the edge of a disk of mass $$M = 3.2\,	ext{kg}$$ and radius $$R = 0.5\,	ext{m}$$, initially at rest. What is the angular velocity $$\omega of $$the disk immediately after the collision?

Accepted Answer

$$\omega = \frac{m v R}{\frac{1}{2} M R^2$ + m R^2$}$$

Question 8

Two flywheels are coupled. The first has moment of inertia $$I_0$$ and angular velocity $$\$$omega_0$$. The second, at rest, has moment of inertia 3I_0$. What is the final angular velocity $$\omega_f$$ after coupling?

Accepted Answer

$$\omega_f = \frac{\$$omega_0$$}{4}$$

Question 9

Which equation represents the first equilibrium condition for static equilibrium of a rigid body?

Accepted Answer

$$\sum_k \vec{F}_k = \vec{0}$$

Question 10

A car with a 2.5-m wheelbase has 52% of its weight on the front wheels and 48% on the rear wheels. Where is the center of mass (CM) located with respect to the rear axle?

Accepted Answer

$$x = 1.2\,	ext{m}$$

Question 11

Which equation represents the second equilibrium condition for static equilibrium of a rigid body?

Accepted Answer

$$\sum_k \vec{	au}_k = \vec{0}$$

Question 12

A mass segment $$\Delta m$$ located at $$\vec{r}_i$$ with velocity $$\vec{v}_i in a $$rotating rigid body has angular momentum $$\vec{L}_i. $$Which formula gives $$\vec{L}_i$$?

Accepted Answer

$$\vec{L}_i = \vec{r}_i 	imes \Delta m \vec{v}_i$$

Question 13

If $$\frac{d\vec{L}}{dt} = 0$$, what does this imply about the angular momentum $$\vec{L}$$?

Accepted Answer

$$\vec{L} is $$constant in time

Question 14

A gymnast on a rotating platform changes her body position, decreasing her moment of inertia. What happens to her angular velocity if angular momentum is conserved?

Accepted Answer

Her angular velocity increases

Question 15

In a collision where a bullet embeds in a disk, which physical quantity is conserved?

Accepted Answer

Angular momentum

Question 16

A car's center of mass is located $$x$$ meters from the rear axle. If the wheelbase is $$d$$ and the front wheels support $$F_F = 0.52w$$, what is $$x$$?

Accepted Answer

$$x = 0.52d$$

Question 17

Which scenario best illustrates conservation of angular momentum in real life?

Accepted Answer

A figure skater spinning faster by pulling in her arms

Question 18

If a system of $$N$$ particles has total angular momentum $$\vec{L} = \vec{L}_1 + \vec{L}_2 + \cdots + \vec{L}_N$$, and no external torque acts, what happens to $$\vec{L}$$?

Accepted Answer

$$\vec{L}$$ remains constant

Angular Momentum and Static Equilibrium: Study Notes

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