$\mathbf{E}(\mathbf{r},t)={\mathbf{E}}_{0}{e}^{i({k}_{0}z-{\omega}_{0}t)}$

daniellex0x0xto
2022-08-05
Answered

Why is it that when one considers some plane wave:

$\mathbf{E}(\mathbf{r},t)={\mathbf{E}}_{0}{e}^{i({k}_{0}z-{\omega}_{0}t)}$

$\mathbf{E}(\mathbf{r},t)={\mathbf{E}}_{0}{e}^{i({k}_{0}z-{\omega}_{0}t)}$

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Why center of mass constant is zero?

$\begin{array}{}\text{(1)}& {\overrightarrow{P}}^{\prime}=\sum ({m}_{i}{\overrightarrow{v}}_{i}^{\prime})=\sum {\textstyle [}{m}_{i}({\overrightarrow{v}}_{i}-\overrightarrow{u}){\textstyle ]}=\overrightarrow{P}-M\overrightarrow{u}=0\end{array}$

$\begin{array}{}\text{(1)}& {\overrightarrow{P}}^{\prime}=\sum ({m}_{i}{\overrightarrow{v}}_{i}^{\prime})=\sum {\textstyle [}{m}_{i}({\overrightarrow{v}}_{i}-\overrightarrow{u}){\textstyle ]}=\overrightarrow{P}-M\overrightarrow{u}=0\end{array}$

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What can we tell about Torque from the equation τ = F R sinɸ, where F is the torquing force, R is the distance from the pivot point to where the force is applied, and ɸ is the angle between the two?

What can we tell about Torque from the equation τ = F R sinɸ, where F is the torquing force, R is the distance from the pivot point to where the force is applied, and ɸ is the angle between the two?

Select one:

a.

Torque is proportional to the force applied

b.

Torque depends on where the force is applied (the distance to the pivot point)c.Torque depends on the angle between the applied force vector and the vector pointing from the pivot point to where the force is applied

d. All of the above

Remembering that $\ell =R\mathrm{sin}\varphi $ and $\tau =F\ell $ if we are given a certain torquing force, 10 N, to act on a wheel of radius 2m, what is the maximum torque we can apply?

Select one:

a. $20N\cdot m$

b. $0N\cdot m$

c. $5N\cdot m$

d. $10N\cdot m$

For linear equilibrium, net force, $F=ma=0$, by newton's second law. What would Newton's Second Law for Rotations be for a system in rotational equilibrium? i.e. how can we express the net torque for a system with constant angular velocity? Let τ represent net torque, α represent angular velocity, I represent moment of inertia, and m and a represent mass and linear acceleration as usual.

Select one:

a. $\tau =ma=0$ because $m=0$

b. $\tau =I\alpha =0$ because $\alpha =0$

c. $\tau =ma=0$ because $a=0$

d. $\tau =I\alpha =0$ because $I=0$

The idea of the force multiplier in torque is sometimes referred to as leverage. There is a famous quote from Archimedes that goes, 'Give me a fixed point and a lever long enough and I shall move the world.' How can we understand this in terms of leverage?

Select one:

a. Long levers are not useful

b. Long levers can generate large forces

c. Leverage doesn't matter when torquing forces are applied

d. Leverage has little read-world application

How does Conservation of Angular Momentum help to produce seasons on Earth?

Select one:a. Conservation of Angular Momentum results in the Earth orbiting closer to the Sun in the Summer

b. The Earth’s rotational axis points in the same direction in space throughout its orbit around the Sun due to Conservation of Angular Momentum

c. The Earth’s rotational axis points in a different direction each 6 months due to Conservation of Angular Momentum

d. Conservation of Angular Momentum results in the Earth's rotational axis always pointing towards the Sun

What can we tell about Torque from the equation τ = F R sinɸ, where F is the torquing force, R is the distance from the pivot point to where the force is applied, and ɸ is the angle between the two?

Select one:

a.

Torque is proportional to the force applied

b.

Torque depends on where the force is applied (the distance to the pivot point)c.Torque depends on the angle between the applied force vector and the vector pointing from the pivot point to where the force is applied

d. All of the above

Remembering that $\ell =R\mathrm{sin}\varphi $ and $\tau =F\ell $ if we are given a certain torquing force, 10 N, to act on a wheel of radius 2m, what is the maximum torque we can apply?

Select one:

a. $20N\cdot m$

b. $0N\cdot m$

c. $5N\cdot m$

d. $10N\cdot m$

For linear equilibrium, net force, $F=ma=0$, by newton's second law. What would Newton's Second Law for Rotations be for a system in rotational equilibrium? i.e. how can we express the net torque for a system with constant angular velocity? Let τ represent net torque, α represent angular velocity, I represent moment of inertia, and m and a represent mass and linear acceleration as usual.

Select one:

a. $\tau =ma=0$ because $m=0$

b. $\tau =I\alpha =0$ because $\alpha =0$

c. $\tau =ma=0$ because $a=0$

d. $\tau =I\alpha =0$ because $I=0$

The idea of the force multiplier in torque is sometimes referred to as leverage. There is a famous quote from Archimedes that goes, 'Give me a fixed point and a lever long enough and I shall move the world.' How can we understand this in terms of leverage?

Select one:

a. Long levers are not useful

b. Long levers can generate large forces

c. Leverage doesn't matter when torquing forces are applied

d. Leverage has little read-world application

How does Conservation of Angular Momentum help to produce seasons on Earth?

Select one:a. Conservation of Angular Momentum results in the Earth orbiting closer to the Sun in the Summer

b. The Earth’s rotational axis points in the same direction in space throughout its orbit around the Sun due to Conservation of Angular Momentum

c. The Earth’s rotational axis points in a different direction each 6 months due to Conservation of Angular Momentum

d. Conservation of Angular Momentum results in the Earth's rotational axis always pointing towards the Sun

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