Some questions concerning centripetal force.

[wtf_albino]

1. A mass attached to a 50-cm long string starts from rest and is rotated 40 times in 1.00 min before reaching a final angular speed. Determine the angular acceleration of the mass, assuming that it is constant.



W = Delta Theta/Delta Time
Average Acceleration = Delta W/Delta time
W = Wo + at
Theta = Wo(t) + 1/2at^2
W^2 = Wo^2 + 2a(Theta)



3. I started by finding W. It said that the wheel made 40 revolutions in 1 minute so i put:

40 Rev/60 s : 2(pi)/rev

and from this i got: 4.2 Rad/s

Using this i used the formula W = Wo + at:

4.2 = 60a
.07 rev/s^2 = A


the answer in the book says .14 rad/s^2 can anyone point out my mistake?

 

[carbz]

I would suggest to check your units. Since you're finding acceleration, the units must match to a unit of acceleration. Please check on that.

 

[Doc Al]

W = Delta Theta/Delta Time

Unless the angular speed is constant, this gives you average speed.

I started by finding W. It said that the wheel made 40 revolutions in 1 minute so i put:

40 Rev/60 s : 2(pi)/rev

and from this i got: 4.2 Rad/s

That's the average angular speed, not the final speed.

Using this i used the formula W = Wo + at:

This equation requires the initial and final angular speeds, not average speed.

Hint: Since the angular acceleration is uniform, there is a simple relationship between the average speed (which you calculated) and the initial and final speeds. What is it?

 

[wtf_albino]

Hint: Since the angular acceleration is uniform, there is a simple relationship between the average speed (which you calculated) and the initial and final speeds. What is it?

hm.. I read through the section covering this part but i couldn't get anything.. could i get another hint?

 

[carbz]

Try to remember the formulas that you learned. There are two formulas that you could use, although there is one that is prefered.

 

[Doc Al]

All is revealed here: https://www.physicsforums.com/showpost.php?p=905663&postcount=2"

 

[wtf_albino]

thanks a lot doc and carbz, ill definitely check it out.

 

[wtf_albino]

sorry, I'm still not seeing it.

 

[Doc Al]

There are two ways to do this problem:
(1) You can continue the way you started, once you figure out the final speed. That list of kinematic equations has one that relates initial and final speed to average speed.
(2) You can make use of a different kinematic formula, one that directly relates distance, time, and acceleration. That too is on the list I provided.