I do not know if I'm allowed to post more than one question, but I have four. Please check out my method (make sure I am going in the right direction, or if I need help). Sorry in advance for my bad latex

**1. Homework Statement**

Compare the linear and angular velocities of the moon around the earth between 1912 and now if the average distance is 3.84x10

^{5}km, average linear velocity is 3.68x10

^{3}kph

and the distance from the moon to the Earth in 1912 was 3.56x10

^{5}km, and the 2009 distance is 4.07x10

^{5}km

(I don't even know if these are accurate numbers, but they're the ones I was given)

**2. Homework Equations**

[tex]v_{T}= r\omega[/tex]

**3. The Attempt at a Solution**

This was the only equation that seemed to pertain to the question. The thing I am confused about is finding the different variables for different dates

To find the angular velocities in the different years, I did

[tex]\frac{v_{T}}{r_{1912}}= \omega_{1912} }[/tex] for 1912 and I got 1.03x10

^{-2}kph

and

[tex]\frac{v_{T}}{r_{2009}}= \omega_{2009} }[/tex] for 2009 and I got 9.04x10

^{-3}kph

They seem like really small numbers...

For the linear velocities, I assumed that [tex]\frac{v_{Tavg}}{r_{avg}}=\omega_{avg}[/tex] and got 9.58x10

^{-3}kph

With the number from that, I plugged that into

[tex]v_{T1912}=r_{1912}\omega_{avg} [/tex] and got 3410.5kph

and

[tex]v_{T2009}=r_{2009}\omega_{avg} [/tex] and got 3899.1 kph

**1. Homework Statement**

A ball with a radius of 2m and mass of 1x10

^{4}kg rolls down an incline plane with an angular acceleration of 6.13rad/s

^{2}

What is the torque acting on the ball, and the linear/angular velocities at the bottom of the plane?

**2. Homework Equations**

see below

**3. The Attempt at a Solution**

I honestly have not tried this problem, and I do not know which equations to use. Seems to me, that I would need an angle of the inclined plane to even do anything with this problem, but there literally is none. If somebody could give me a hint, I have my paper and pencil ready to go, as well as a calculator.

**1. Homework Statement**

A string has an 89N tensile strength. One end of a 1m piece of this string is tied to a 4.54kg toy car. The other end is attached to a ring slipped over a pole so that the car can rotate around it freely. Calculate the maximum angular speed of the car without breaking the string. How many revolutions does the car travel in 1 minute (friction neglected)?

**2. Homework Equations**

[tex]F_{c}=mr\omega^{2}[/tex]

[tex]\omega=\frac{d\theta}{dt}[/tex]

**3. The Attempt at a Solution**

Using the first equation, I solved for omega getting

[tex]\omega=\sqrt\frac{F_{c}}{mr}[/tex]

[tex]\omega=\sqrt\frac{89N}{4.54}[/tex]

Getting 4.42rad/s

I wasn't quite sure on the revolutions part, although it should be simple. I'm fairly sure I'm incorrect. I did

[tex]\omega=\frac{d\theta}{dt}[/tex] so (4.42)(60s)=revolutions, and I got 265.2

Seems like too much, so I converted it into radians, and got 4.63 which is in my opinion a more feasible answer, but I thought I was in radians already...

**1. Homework Statement**

A 10m centrifuge can spin at a linear velocity of 17.3 m/s and brake to a stop in 80 seconds

a)What is the torque produced?

b)What is the centripetal acceleration?

c)What is the centripetal force an an 80kg astronaut?

**2. Homework Equations**

torque, see below

[tex]a_{c}=\frac{v_{T}^{2}}{r}[/tex]

[tex]F_{c}=\frac{mv_{T}^{2}}{r}[/tex]

**3. The Attempt at a Solution**

This is another one that I have not tried. I still feel like I'm not given enough information. How can I find the torque without a force (a mass to find the force). I can't use the 80kg astronaut, as far as I know, otherwise it would have been the first question asked.

For the others, it looks like I could just plug and chug into the equations.

Please and thank you!