Centripetal Acceleration while Swinging a Stone on a String

[singh101]

Homework Statement

I can't seem to figure out the answer for this question with formulas given.

Relevant Equations

Angle of rot= arc length/ radius
Angular velocity= angle of rotation/ time
v=rw (v=tangential veloctity) (w=angular velocity) r= radius
centripe acceleration= v^2/r

So my initial understanding is that it completes 5 revolutions per second. I converted the 5 rev to radians, so each revolution is 2pi. Now since I got angle of rotation I can plug it into the angular velocity formula which is Angular velocity= angle of rotation/ time. However since I don't have time I can change the formula to angle of rot x frequency. Frequency in this case would be 5. So ang Velocity is 10pi rad/s. From their on I get the tang velocity and plug it into the centrip acceleration formula, however I keep getting the wrong answer. Is there anyway to solve this with the equation given below or am I missing any equations.

 

[haruspex]

So ang Velocity is 10pi rad/s.

Right so far.

From their on I get the tang velocity and plug it into the centrip acceleration formula, however I keep getting the wrong answer.

I cannot tell where you went wrong if you do not show your detailed working.

 

[singh101]

my question is that is 2pi the angle of rotation or is that the angular velocity.

 

[singh101]

Oh wait I think I figured out my mistake. The 5 revolutions per second is the frequency am I correct? How would that be stated as a period

 

[haruspex]

my question is that is 2pi the angle of rotation or is that the angular velocity.

There is no specific angle of rotation in the question, only a rate: 5 revs/s $=10\pi^c/s$, where the c denotes radians.

 

[haruspex]

Oh wait I think I figured out my mistake. The 5 revolutions per second is the frequency am I correct? How would that be stated as a period

The rotation period is the time to complete one revolution.

 

[haruspex]

so is the 5 revolution per second the frequency or period. I am assuming that is the frequency. If it is the frequency then what would the period be stated as if it were given in the question.

5 revs/s is the rotation rate. "Frequency" needs to be distinguished from "angular frequency ". The frequency is the number of revolutions per unit time, 5 per second, whereas angular frequency is the number of radians per unit time.
In equations like $v=\omega r$ and $a=\omega^2r$ use the angular frequency.

 

[singh101]

oh ok so 5rev/s can be converted into rad by multiplying it by 2pi which gives is 10pi rad/s. This then in added to the formula v=rw. so w is 10pi x 0.4. which gives us 4pi. This is then put into the formula v^2/r (4pi)^2/0.4= 40m/s^2. Am I correct?

 

[haruspex]

oh ok so 5rev/s can be converted into rad by multiplying it by 2pi which gives is 10pi rad/s. This then in added to the formula v=rw. so w is 10pi x 0.4. which gives us 4pi. This is then put into the formula v^2/r (4pi)^2/0.4= 40m/s^2. Am I correct?

Yes. Or you can use $\omega^2r$ for the centripetal acceleration instead, skipping finding v.

 

[singh101]

Oh ok thank you so much I understand where I made the mistake.