Solving Spinning Slingshot Homework: Initial Velocity & Components

[Just_enough]

Homework Statement

A rock initially at rest in a sling of length r meters is
brought to a speed of n rotations per second after three complete revolutions. It is then released , leaving the sling at an angle of θ above horizontal.

When the rock is released, write the initial velocity and
its horizontal and vertical components in terms of the variables provided above

given equation:

https://gyazo.com/1541ea407be0853d58465bed8abc9c82

my question is isn't the Accel tan of whn the sling is release = Vi? if not, why and how can I get the Vi?

 

[gneill]

Hi Just_enough, Welcome to Physics Forums/

my question is isn't the Accel tan of whn the sling is release = Vi? if not, why and how can I get the Vi?

Your question is not clear; please use complete words, not abbreviations. Can you restate it and show what you've already tried? What is your understanding of information that you are given in the problem statement?

 

[Just_enough]

Hi Just_enough, Welcome to Physics Forums/Your question is not clear; please use complete words, not abbreviations. Can you restate it and show what you've already tried? What is your understanding of information that you are given in the problem statement?

That all I was asked (mostly what I am confused on). I've upload the assignment as an attachment. but basically how do I find the initial velocity after the sling has been released? I think that the acceleration tangent of when the sling is spin is equal to the velocity initial after it's release is it not?

 

[haruspex]

the acceleration tangent of when the sling is spin is equal to the velocity initial

An acceleration cannot equal a velocity. How is the angular velocity related to the linear velocity?

By the way, the question is flawed. It asks for the average angular acceleration, suggesting that the acceleration is not constant, or need not be constant to answer the question. But you are given the initial and final angular velocities and the angle traversed, not the time taken. It is not possible to deduce the time taken or the average angular acceleration from that information. For example, the stone might be spun around slowly for 2.9 revolutions, then given a huge acceleration at the end. That would take longer than with a constant acceleration, yet satisfy all the given conditions.
To solve the question it will be necessary to assume that the acceleration is constant.

 

[CWatters]

The problem statement actually asks a series of questions that you didn't mention or answer. Like many multi step problems it has been designed to lead you towards the final answer. If you haven't already done so I would work through them all one at a time.

 

[Just_enough]

An acceleration cannot equal a velocity. How is the angular velocity related to the linear velocity?

I don't know, I am dumb with it comes to physics

An acceleration cannot equal a velocity. How is the angular velocity related to the linear velocity?
It is not possible to deduce the time taken or the average angular acceleration from that information.

So I should tell me professor to give us a time?

The problem statement actually asks a series of questions that you didn't mention or answer. Like many multi step problems it has been designed to lead you towards the final answer. If you haven't already done so I would work through them all one at a time.

I have (hopefully it's correct) but I don't see a connect those and this question

 

[haruspex]

So I should tell me professor to give us a time?

No, since time is asked for. I suggest stating "assuming constant angular acceleration" and proceding on that basis. If the prof objects that the assumption is unnecessary, give her my proof that it is.

 

[Just_enough]

No, since time is asked for. I suggest stating "assuming constant angular acceleration" and proceding on that basis. If the prof objects that the assumption is unnecessary, give her my proof that it is.

lol sorry, I do not follow. should I start with that quote and say that the projectile could be spun slowly within 3 rev, that it's not possible to find the average acceleration without a given time it take for the projectile to spin 3 rev? also is this needed in order to find initial velocity of when the person release the projectile after spinning it?

 

[haruspex]

is this needed in order to find initial velocity of when the person release the projectile after spinning it?

No, you can get that easily and directly from the information given.

should I start with that quote and say that the projectile could be spun slowly within 3

State that you are assuming constant angular acceleration, then solve the problem using that assumption. What equations do you know for constant acceleration?
Later, if the prof claims that the assumption was not needed, use the slow starting spin wxample to prove that the assumption is neede.

 

[Just_enough]

No, you can get that easily and directly from the information given.

what? how? I'm sorry, but I'm really slow when it comes to physics. are you referring to using the V0y = V0sinθ equation?

 

[CWatters]

If you are familiar with the equations for linear motion under constant acceleration (eg SUVAT) then those for rotation under constant angular acceleration are similar. It might be worth spending time comparing the two sets of equations as they work in much the same ways.

 

[haruspex]

what? how? I'm sorry, but I'm really slow when it comes to physics. are you referring to using the V0y = V0sinθ equation?

From my post #4:

How is the angular velocity related to the linear velocity?