What Is the Period of a 50-g Weight in Uniform Circular Motion?

[Paulbird20]

Circular path---) finding period

Homework Statement

A 50-g weight tied to a string is twirled in uniform circular motion. If the circumference of the circular path is 207.3 cm and the weight completes 67.1 revolutions per minute, what is the period of the motion, in seconds?

Homework Equations

V= 2* pi* r / T
V= velocity
r= radius
T = period

The Attempt at a Solution

ok so i converted the circumference to the radius first convert to meters = 2.07300 meters

Then divide that by pi to get the diamater then by 2 to get the radius so i arrive at .330095 as the radius.

Where i am stuck is how to convert the revolutions per minute to the velocity and I am sure the weight comes into play . Any tips would be great thanks.

 

[Nabeshin]

Think about the information you are given. What does the fact that the weight completes 67.1 revolutions per minute mean? What are the units on this, and what are the units on period?

 

[Paulbird20]

the units on period is seconds but i don't see how i can use revolutions and the weight to obtain the velocity

 

[Nabeshin]

And what are the units on the 67.1 revolutions per minute? Do you know what these units correspond to? You're trying very hard to apply a formula which isn't the best formula to apply for this given problem.

 

[Paulbird20]

because trying to find period i would have t = 2 * pi * r / v

so the meters from radius and velocity cancel leaving seconds.
But i yet to see how weight comes into play

 

[RoyalCat]

the units on period is seconds but i don't see how i can use revolutions and the weight to obtain the velocity

And what is the relation between the revolutions per minute and the period?
The magic of it all is that the weight doesn't come into play. :)

 

[Paulbird20]

that was the equation provided by the instructor =(

 

[Nabeshin]

Ok, the units on period are seconds but it's actually seconds/revolution, right?

Now, you have a piece of information about revolutions/minute...

 

[Paulbird20]

2pi radians = 1 revolution so that's 60 seconds per 2 pi radiants so that's 10.679 radiants

 

[Nabeshin]

Why are you converting into radians? Okay... let's see, you have the following:
$$\frac{67.1 Revolutions}{minute}$$

Your answer is a period, which is going to be of the form
$$\frac{seconds}{revolution}$$

So, your mission is basically to convert the first into the form of the second...

 

[RoyalCat]

2pi radians = 1 revolution so that's 60 seconds per 2 pi radiants so that's 10.679 radiants

Be careful, you're mixing a lot of things up.

This is what's relevant for you:

$$1 \frac{revolution}{minute}= \frac{2\pi radians}{60 seconds} = \tfrac{1}{60}\frac{revolutions}{second}$$

What you calculated just has my head spinning. @@

 

[Paulbird20]

i got .117 for the period

67.1 * 2pi / 60 * 1/60

 

[RoyalCat]

i got .117 for the period

67.1 * 2pi / 60 * 1/60

That is incorrect. Remember, the period is in $$\frac{revolutions}{second}$$
And NOT in $$\frac{radians}{second}$$
You don't need to substitute the revolutions with $$2\pi$$

Just for reference, I got $$V\approx 1.456 \tfrac{m}{s}$$
What's the textbook's answer?