4. In the figure, Block \( B \) is released from rest and attains a linear velocity of \( 9.81 \mathrm{~m} / \mathrm{sec} \) in 10 seconds. How many revolutions has drum \( A \) turned in this time?
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The motor $A$ accelerates uniformly from zero to 3600 rev/min in 8 seconds after it is turned on at time $t=0 .$ It drives a fan (not shown) which is attached to drum $B$. The effective pulley radii are shown in the figure. Determine (a) the number of revolutions turned by drum $B$ during the 8 -second startup period, ( $b$ ) the angular velocity of drum $B$ at time $t=4 \mathrm{s},$ and $(c)$ the number of revolutions turned by drum $B$ during the first 4 seconds of motion. Assume no belt slippage.
A drum rotates around its central axis at an angular velocity of $12.60 \mathrm{rad} / \mathrm{s}$. If the drum then slows at a constant rate of $4.20$ $\mathrm{rad} / \mathrm{s}^{2}$, (a) how much time does it take and (b) through what angle does it rotate in coming to rest?
An elevator cable winds on a drum of radius $90.0 \mathrm{cm}$ that is connected to a motor. (a) If the elevator is moving down at $0.50 \mathrm{m} / \mathrm{s},$ what is the angular speed of the drum? (b) If the elevator moves down $6.0 \mathrm{m},$ how many revolutions has the drum made?
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