math

[saraa82]

The circular blade on a saw has a diameter of 7.4 inches and rotates at 2503 revolutions per minute. 1) Find it's angular speed in units of rad/s. 2) Find the speed of the saw teeth in feet per second as they contact the wood being cut, answer in units of ft/s.

I have no clue how to do this please help!!!

 

[tkhunny]

Start with the circumference of the blade.

You must have some idea. It's a circle. Dump everything you know about circles.

 

[saraa82]

circumference=pi d, so it would be 23.24778564

then could i do 2503/23.245 to get 107.666 and then divide by 60 to get it in seconds? 1.7944?

 

[burakaltr]

The circular blade on a saw has a diameter of 7.4 inches and rotates at 2503 revolutions per minute. 1) Find it's angular speed in units of rad/s. 2) Find the speed of the saw teeth in feet per second as they contact the wood being cut, answer in units of ft/s.

I have no clue how to do this please help!!!

2503*2*PI/60= 261.88 rad/s

(dtheta/dt )=261.88
dtheta=261.88 dt

12 inch= 1 ft
3.7 inch=3.7/12=0.308 ft
r*dtheta=261.88*0.308* dt
r*dtheta/dt= 80.7
r*dtheta=80.7 *dt

 

[burakaltr]

2503*2*PI/60= 261.88 rad/s

(dtheta/dt )=261.88
dtheta=261.88 dt

12 inch= 1 ft
3.7 inch=3.7/12=0.308 ft
r*dtheta=261.88*0.308* dt
r*dtheta/dt= 80.7
r*dtheta=80.7 *dt

r*dtheta=v*dt
v=r*261.88
v=0.308*261.88

v= 80.66 ft/s

 

[Deleted member 4993]

The circular blade on a saw has a diameter of 7.4 inches and rotates at 2503 revolutions per minute. 1) Find it's angular speed in units of rad/s. 2) Find the speed of the saw teeth in feet per second as they contact the wood being cut, answer in units of ft/s.

I have no clue how to do this please help!!!

w = 2503 rev/min = 2503*2*π/60 rad/sec = 262.1 rad/sec

v = r * w = 3.7 * 262.1 in/sec = 3.7 * 262.1/12 ft/sec = 80.81 ft/sec

 

[jsterkel]

Labels

circumference=pi d, so it would be 23.24778564

then could i do 2503/23.245 to get 107.666 and then divide by 60 to get it in seconds? 1.7944?

I recommend you keep track of the labels. They will help you make sure your answer is right, and may point you in the right direction.

Using your work as a starting point....
pi*d = circumference
d is in inches, so circumrerence is 23.24 inches. We need ft/s, so lets convert this to ft.
23.24 inches = 1.936667 ft

The speed of the saw is revolutions per minute, but we need seconds. So lets divide by 60 to get rev per second.
2503 rev / minute = 41.7 rev/sec

Now that we have our labels closer to what we need,

41.7 rev/ second * 1.9366667 ft / rev = 80.76 ft / sec (note - the revolutions cancel each other)

rev/sec * ft/rev = (rev * ft)/ (sec * rev) = ft/sec.

I hope this helps and is understandable.