F16-6. For a short period of time, the motor turns gear A with a constant angular acceleration of a = 4.5 rad/s², starting from rest. Determine the velocity of the cylinder and the distance it travels in three seconds. The cord is wrapped around pulley D which is rigidly attached to gear B. 225 mm 75 mm 125 mm a = 4.5 rad/s Ad C.

a - 12 rad/s 16-3. B The disk is originally rotating at e, = 12 rad/s If it is subjected to a constant angular acceleration of a = 20 rad/s, determine the magnitudes of the velocity and the n and f components of acceleration of point A at the instant t = 2s 04 m 0.5 m-A

The slotted arm AB drives pin "C" through the spiral groove described by the equation r = = (30) ft, where "0" is in radians. If the arm starts from rest when 0 = 60° and is driven at an angular velocity of 8 = (4t) rad/s, where "t" is in seconds, determine the radial and transverse components of velocity and acceleration of the pin "C" when t = 1 s. B C Ans. a₁ = -134.3 ft/s² Ans. ā= 132.6 ft/s²

A motor gives gear A an angular acceleration of αA=0.006θ^2 rad/s2, where θ is in radians. If this gear is initially turning at ωA=10 rad/s, Determine the angular displacement of gear A at the instant at which gear A reaches angular velocity of 35 rad/s. Determine the angular velocity and acceleration of gear B at this instant.   Find the magnitude of acceleration of point P on the pitch circle of gear B at this instant.

At a given instant the top BB of the ladder has an acceleration aBaBa_B = 2.1 ft/s2ft/s2 and a velocity of vBvBv_B = 4.0 ft/sft/s , both acting downward Determine the acceleration of the bottom AA of the ladder. Determine the ladder's angular acceleration at this instant.

The hydraulic cylinder gives pin A a constant velocity v = 2.0 m/s along its axis for an interval of motion and, in turn, causes the slotted arm to rotate about O. Determine the values of r, r, and 0 for the instant when 0 = 32°. (Hint: Recognize that all acceleration components are zero when the velocity is constant.) Answers: r = 7 = 0 = A i i i 0 34 260 mm- m/s m/s² rad/s²

The disk rotates about the shaft SS, while the shaft is turning about the zz axis at a rate of ωzωzomega_z = 6 rad/srad/s , which is increasing at ααalpha = 2.5 rad/s2rad/s2 . No slipping occurs. Determine the xx, yy, and zz components of the velocity of point BB on the disk at the instant shown using scalar notation. Determine the xx, yy, and zz components of the acceleration of point BB on the disk at the instant shown using scalar notation.