# Dynamics Physics - Acceleration Analysis / Gear Ratios /

by f2434427@rmqkr
Tags: acceleration, analysis, dynamics, gears, physics
 P: 3 First time posting. 1. The problem statement, all variables and given/known data Gears A and B, of Masses 4kg and 10kg, respectively, are rotating about their mass centers. The radius of gyration about the axis of rotation is 100mm for A and 300mm for B. A constant couple of C=0.75Nm acts on gear A. Neglecting friction, compute: - Angular Acceleration of each gear - Tangential contact force between the gears at C May want to look at attachment for image. 2. Relevant equations 3. The attempt at a solution Started with the smaller gear. Using T=I$\alpha$ , where I=mr^2 Rearrange the equation to get $\alpha$ = 0.75 / (4*0.1^2) = 18.75 rad/s^2 Not to sure how to draw a relationship with the 2nd larger gear. Maybe using w1/w2 = r2/r1 then $\alpha$ = w^2 * r Thanks, Attached Thumbnails
 Homework Sci Advisor HW Helper Thanks PF Gold P: 10,285 Welcome to PF; The applied torque has to accelerate both gears doesn't it? If this were a linear case, you'd use a free body diagram to couple the masses wouldn't you?
 P: 3 Ah yes, that would make sense. Forgot to account for the 2nd gears inertia hmm. Dont quite understand what you mean by coupling the masses though
Homework
HW Helper
Thanks
PF Gold
P: 10,285

## Dynamics Physics - Acceleration Analysis / Gear Ratios /

When you push on one mass, it pushes on the other one .. the masses are said to be coupled ... the motion of one affects the motion of another.
 P: 3 Alrighty, Well the force applied from gear A, will have an opposite reaction on Gear B. T=F*d F=0.75/0.15 = 5n then applying this force to Gear B. T=F*D = 5 * 0.45 = 2.25 Nm alpha = T/I = 2.25/(10*0.3^2) =2.5 rad/s^2 Looks about right to me..... hopefully. Logically, first gear would have to spin faster than the 2nd.
 Homework Sci Advisor HW Helper Thanks PF Gold P: 10,285 That's right - the smaller gear will reach a higher angular velocity in the same time, so must have a higher acceleration. You should be able to see from the relative sizes how the accelerations are related.

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