A single pulley having both an inner and outer rim is pin connected to the block

Question

A single pulley having both an inner and outer rim is pin connected to the block at A. As cord CF unwinds from the inner rim of the pulley with the motion shown, cord DE unwinds from the outer rim. Suppose that v_F = 3 m/s, a_F = 3 m/s^2, r_dinner = 30 mm, and r_router = 60 mm. (Figure 1) Determine the angular acceleration of the pulley at the instant shown measured counterclockwise. Express your answer using three significant figures. Enter positive value if the angular acceleration is counterclockwise and negative value if the angular acceleration is clockwise. Alpha = Determine the acceleration of the block at the instant shown. Express your answer to three significant figures and include the appropriate units. a_x =

Explanation / Answer

Suppose pulley is rotating with angular velocity w and angular acc. alpha.

then aF = alpha x Rin

3 = alpha ( 0.030)

alpha = 100 rad/s^2 ...........Ans (A)

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B.

ax = aD - aF

aD = (alpha) (Rout) = 100 x 0.060 = 6 m/s^2

ax = 6 - 3 = 3 m/s^2

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