# Circular saw

#### mathieumg

We have a circular saw of radius 250 mm.

The speed at its border is of 50 m/s.

When we cut the power, it takes the saw 8 seconds to completely immobilize with a constant deceleration.

How many turns has the saw done before it completely stopped?

I did :

c = 2*pi*0.25m = 1.57m

x = 1/2 * (50m/s + 0m/s) * 8s

The number of turns should be equal to x/c = 200m/1.57m = 127.39 turns

But the answer given by the manual is 3 * 127.39 = 382 turns

What have I done wrong to be short by a factor of 3? Or is it just the manual that is wrong? Because I've looked every possible avenue and can't find what isn't right.

Thanks a lot!

#### r.samanta

i dont know , but my answer is coming what you got =127.32 revolutions

• mathieumg

#### topsquark

Forum Staff
We have a circular saw of radius 250 mm.

The speed at its border is of 50 m/s.

When we cut the power, it takes the saw 8 seconds to completely immobilize with a constant deceleration.

How many turns has the saw done before it completely stopped?

I did :

c = 2*pi*0.25m = 1.57m

x = 1/2 * (50m/s + 0m/s) * 8s

The number of turns should be equal to x/c = 200m/1.57m = 127.39 turns

But the answer given by the manual is 3 * 127.39 = 382 turns

What have I done wrong to be short by a factor of 3? Or is it just the manual that is wrong? Because I've looked every possible avenue and can't find what isn't right.

Thanks a lot!
I also agree, though I think the solution would be better expressed in terms of the relevant theta's and omega's.

-Dan

• mathieumg

#### mathieumg

Ok, thank you both for confirming I am still sane I shall skip this number!

Dan, I am revising my old mechanics manual for an upcoming diagnostic exam and at this point in the manual, they have only mentionned regular kinematics and tengential acceleration, so I figured it had to be solvable using regular kinematics even though I'm aware of the circular equations #### Paul46

I get the same answer too.

((u + v)/2) * t = s = 200m

200/ circumference = 127.32 revolutions

You can also use this formula:

Find the rps (revs per sec) = 31.83

(rps*t)/2 = 127.32

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• mathieumg

#### tinkerzircon

We have a circular saw of radius 250 mm.

The speed at its border is of 50 m/s.

When we cut the power, it takes the saw 8 seconds to completely immobilize with a constant deceleration.

How many turns has the saw done before it completely stopped?

I did :

c = 2*pi*0.25m = 1.57m

x = 1/2 * (50m/s + 0m/s) * 8s

The number of turns should be equal to x/c = 200m/1.57m = 127.39 turns

But the answer given by the manual is 3 * 127.39 = 382 turns

What have I done wrong to be short by a factor of 3? Or is it just the manual that is wrong? Because I've looked every possible avenue and can't find what isn't right.

Thanks a lot!