4. The system shown starts from rest, and each component moves with a constant acceleration. If the relative acceleration of block C with respect to collar B is 60 mm/s² upward and the relative acceleration of block D with respect to block A is 110 mm/s² downward, determine, (a) The kinematic constraints for the blocks, (b) Acceleration of blocks A, B, C, and D (c) the velocity of block C after 3 s, (d) the change in position of block D after 5 s. A D B C Figure 4: Weight-pulley system

1) Near the end of its takeoff roll, the airplane is "rotating" (nose pitching up) just prior to liftoff. The velocity and acceleration of the aircraft, expressed in terms of the motion of the wheel assembly C, are Vc and ac, both directed horizontally forward. The pitch angle is 0, and the pitch rate w = ė is increasing at the rate a = w . If a person A is walking forward in the center aisle with velocity L and acceleration L , both measured forward relative to the cabin, calculate the components of the position, velocity and acceleration vectors in the inertial frame shown as OXY (ground-fixed). Y Y Xc Xc Origin of the Bxy frame is at the point B, and the point C of this frame has a position Xc, velocity Vc, and acceleration ac with respect to the inertial frame OXY. L W = 0 (DEGREE/S) . (DEGREE/S²) XC Vc ac L a = ) (m) (km/h) (m/s²) (m) (m) | (m/s) . (m/s²) (DEGREE) 3,6 16 1660 235 22 20 10 3

a) A flywheel with a diameter of 356 mm accelerates uniformly from rest at a rate of 2.5 rad/s² for a period of 1.8 minute. It then continues at the maximum speed attained for a further period of 4.5 minutes, after which it decelerates uniformly to rest over a final period of 2.8 minutes. Calculate for the flywheel: (a) The maximum angular velocity attained in rad/s and also in rev/min. (b) The rate of deceleration during the final period of the motion. (c) The angle, given in radians, turned through by the flywheel during its period of acceleration.

3. The normal component of acceleration represents a. the time rate of change in the magnitude of the velocity b. the time rate of change in the direction of the velocity c. magnitude of the velocity d. directions of the total acceleration

Consider that at the instant shown, bar AB of the mechanical system below has a angular velocity (wAB) counterclockwise at 5 rad/s and an angular acceleration (alphaAB)counterclockwise 2 rad/s².The length of bar AB is 0.4 m and the length of bar BC is 1 m. For the instant shown, and using a "Analysis of Relative Motion", determine: (a) the speed of point B (b) angular velocity of connecting bar BC (c) the speed of point C (d) the acceleration of point B (d) the acceleration of point C

1. Bug B is crawling radially outward on the spoke of a wheel at a constant speed of 4 cm/s relative to the spoke of the wheel. The center of the wheel (Point C) is also moving to the left at 160 cm/s and accelerating at 120 cm/s². As a result, its angular speed is 8 =4 rad/s and its angular acceleration is = 3 rad/s². At that same time the bug is 30 cm from the center of the wheel and is directly above the center of the wheel. a. What is the velocity vector of the bug relative to the ground at that particular time? b. What is the acceleration vector of the bug relative to the ground at that particular time? 8 = 4 rad/s Ö = 3 rad/s² →X Vc = 160 cm/s ac = V₁ = 4 cm/s 120 cm/s² TAY 30 cm ↓g

Collar B is pinned to arm AB as it slides over a circular guide bar. The guide bar translates to the left such that the distance from pivot A to center C is an arbitrary function of time u(t). Derive expressions for the angular velocity and angular acceleration of arm AB in terms of u. R C В4

Question 2 : A bead M slides without friction on a rigid wire ( T ) .  This rigid wire rotates around the Z axis of a fixed reference frame R ( O , x , y , z ) with constant angular velocity vectorok .  A rotating reference frame R ' ( 0 ' = 0 , üük ) is attached to the rigid wire ( T ) .  a) Determine the velocity and acceleration vectors of the bead M with respect to the rotating frame R' given that its position vector is : 7 - OM - ae , where a is positive constant.  b) Determine the fictitious forces applied to the bead M in the rotating frame R. c) Given that the normal force exerted on the bead M by the rigid wire is: N = N+ NK.  By applying the 2nd Law of Newton in the rotating frame R", deduce the components N and N

A temperature sensor is attached to slider AB which moves back and forth through 60 in. The maximum velocities of the slider are 12 in./s to the right and 30 in./s to the left. When the slider is moving to the right, it accelerates and decelerates at a constant rate of 6 in./s2 ; when moving to the left, the slider accelerates and decelerates at a constant rate of 20 in./s2 . Determine the time required for the slider to complete a full cycle, and construct the v–t and x-t curves of its motion.

Relative analysis in two dimensions and dependent motion: If it is known that the instant shown in block A has a velocity of 8 in/s and an acceleration of 6 in/s², both directed downward on the inclined plane, determine: A) The velocity of block B B) The acceleration of block B