# How to find angle from angular velocity?

1. Apr 10, 2013

### Sneakatone

A cat swipes at a spool of thread, which then rolls across thefloor with an initial speed of 1.5 m/s. The spool deceleratesuniformly to a stop 3 m from its initial position. The spool has aradius of 1.5 cm and rolls without slipping.

a) What is the initial angular velocity?

b) Through what total angle does the spool rotate whileslowing to a stop?
c) What is the angular acceleration during this motion?

I dont really know how to do the rest of the parts.

2. Apr 10, 2013

### dinospamoni

For b) what is the circumference of the spool? How far did it go?

3. Apr 10, 2013

### Ampere

For part b, we are given that the spool travels 3m. The spool rolls along its circumference, right? How many circumferences in 3m? (And how many radians in one circumference)?

4. Apr 10, 2013

### Simon Bridge

a. this is correct - you used vT=rw ... but do you know why this is the case?

b. Get something round and roll it back and forth across a flat surface.
Watch carefully.

What is the relationship between the distance rolled and the amount the object turns?

c. How would you find regular acceleration?
Relationship between the linear acceleration of the edge of the ball and it's angular acceleration is...

5. Apr 10, 2013

### Sneakatone

the circumference is 0.094 m, and it traveled 3 m

there 95.74 circumferences in 3 m

6. Apr 10, 2013

### Ampere

I got the same circumference, but found a different number of circumferences in 3m. How did you calculate 95.74?

Once you have the # of circumferences, you can use the # of radians in one circumference to find the total angle.

7. Apr 10, 2013

### Sneakatone

3/0.094=95.74
should it have been smaller?

8. Apr 10, 2013

### Ampere

3/0.094 isn't 95.74. Are you making a typo somewhere?

9. Apr 10, 2013

### Sneakatone

I must have had the wrong numbers some how.

10. Apr 10, 2013

### Ampere

Yes, and how many radians in each circumference?

11. Apr 10, 2013

### Sneakatone

12. Apr 10, 2013

### Ampere

Aren't there 2pi radians per circumference?

13. Apr 10, 2013

### Sneakatone

31.91/(2pi)=5.07

14. Apr 10, 2013

### Ampere

Other way around. If you have 31.91 circumferences, and 2pi radians/circumference, then you can just multiply.

15. Apr 10, 2013

### Sneakatone

31.91*2pi=200.4

16. Apr 10, 2013

### Ampere

Yes, though if you used unrounded numbers, you'd get exactly 200.

17. Apr 10, 2013

### Sneakatone

so 200 would be the total angle rotated?

18. Apr 10, 2013

### Ampere

19. Apr 10, 2013

### Sneakatone

for part c I know how to solve if there was an extra time given .
would I find time by 3/1.5=2

20. Apr 11, 2013

### Sneakatone

would the equation Ø = w1 t + 1/2 ã t^2 be applied where

Ø - angular displacement
w1 - initial angular velocity
t - time
ã - angular acceleration
??