Question

A 60 mm radium drum is rigidly attached to a 100 mm radius drum as shown. One of the drum rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that end D of the cord
is pulled to the left with a velocity of 160 mm/s and acceleration of 600 mm/s?, both directed to the left, determine the acceleration of points A, B, and C of the drum.
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Answer 1

The acceleration at points A, B and C are respectively; 960 mm²/s, 1600 mm²/s and 600 mm²/s

What is the acceleration?

The drum rolls without sliding and as such its' instantaneous center will lie at B. Thus;

V_d = V_c = 160 mm/s

Also, a_d = a_c = 600 mm²/s

Now, formula for velocity at A is;

V_a = r_ab * ω

where ω = 160/(100 - 60)

ω = 4 rad/s

V_a = 60 * 4

V_a = 240 mm/s

Acceleration at A = V_a²/r_ab

Acceleration at A = 240²/60 = 960 mm²/s

Now, V_b = 100 * 4 = 400 mm/s

Acceleration at B = 400²/100 = 1600 mm²/s

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