Physics Dynamics Question

1. Dec 4, 2008

tom23

1. The problem statement, all variables and given/known data

Gear ‘B’ on the machine shown below accelerates from rest to 250 rpm in 2 seconds. Determine the angular velocity and acceleration of A, and the linear acceleration and velocity of rack C. See image attached

2. Relevant equations

I dunno where i would start off with this question, help would be appreciated.

3. The attempt at a solution

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2. Dec 4, 2008

tiny-tim

Welcome to PF!

Hi tom23! Welcome to PF!

(how far apart are the teeth on B compared with A and C? )

First find the angular velocity and acceleration of B.

Then you know that the "tooth-rates" on A B and C are the same … eg if B rotates through 7 teeth of the cog, then both A and C also move through 7 teeth.

3. Dec 5, 2008

tom23

So I got this until now, is it right?

ang velocity = 250 rpm x 2 pi x (1/60) = 26.2 rad/s

ang acceleration = change in ang velocity / chang in time = 26.2 rad/s / 2s = 13.1 rad/s^2

Thus at B: tangential Velocity at B = ang velocity*radius1 = 26.2*20 = 524 cm/s

tangential Acceleration at B = ang acceler.*radius1 = 13.1*20 = 262 cm/s^2

Therefore on A:

Angul. Velocity at A = tang. velocity/radius2 = 524/15 = 34.9 rad/s
Angul. Acceler at A = tang. acceler./radius2 = 262/15 = 17.5 rad/s

Does this two answers sound right, now how would i go on to solve for linear accel. and velocity of rack C?

4. Dec 5, 2008

tiny-tim

Yes, that's fine.
You haven't answered my question: how far apart are the teeth on B compared with A and C?

Same method … you have the tangential velocity of A, so you can find the linear velocity of C.

5. Dec 5, 2008

tom23

Tey didnt give the distance, so i believe it is the same, so for linear velocit and accel at C, i got:

V = 34.9 (30cm) = 1047 cm/s
a = 17.5 (30cm) = 525 cm/s

Does it look right?

Thanlks for all your help above!

6. Dec 5, 2008

tiny-tim

Hi tom23!
Yes … that's fine … if the teeth are all the same distance apart, then the tangential velocities and the linear velocity are all the same.

(though I'd have done it directly from B … 26.2(40), rather than from A, as you did! )