In the position shown, the disk has an angular velocity of 8 rad/sec in the clockwise direction, and an angular acceleration of 30 rad/s^2 in the counterclockwise direction. y 5 in. B -10 in.: D 12 in. Determine: (a) The angular velocity vector (rad/s) of each rod, BC and CD (b) The angular acceleration vector (rad/s^2) of each rod, BC and CD (c) The acceleration vector (in/s^2) of points B and C

3) Link AB of a robotic arm is rotating at a constant speed of 4 rad/s, while link BC is rotating at 5 rad/s, a speed that is increasing at the rate of 2 rad/s². Find the magnitudes of the velocity and acceleration of point C when AB is vertical and BC is horizontal, as shown here. 2.0 ft 1.5 ft B WAB A WBC = 5 rad/s αBC = 2 rad/s² = 4 rad/s C

The following diagram shows a piston moving in a cylinder with rod AB. Point B is rotating clockwise with an angular velocity of w. cylinder piston A connecting rod crank bearing B ResearchGate The motion of B is given by the equation r = C cos(wt) + Dsin(wt) Were r is the horizontal +vertical distance of B from O, and C, D are constants. For C=D=42mm and w = 20 rad/s. (i) Write r in the form Rcos (wt ± ß) and state the amplitude and period of r. (ii) Sketch one complete cycle of r. (iii) Explore the differences between the derived form and drawn form

4. A wheel having a diameter of 30cm starts from rest and accelerates uniformly to an angular velocity of 900 rpm is 5 sec. Find the position at the mo end of 1sec of a point originally on top of the wheel. ANS: at the bottom 5. A flywheel of radius 30cm starts from rest and rotates with constant angular acceleration of 0.5 rad/s2. Compute the total acceleration of the point on the rim after it has turned through 120°. ANS: 0.65 m/s

8. The constant angular acceleration of the rotating disk is 12 rad/s2. The angular velocity of the disk is 24 rad/s clockwise when t = 0. Determine the total angle turned by the disk between t = 0 and t = 4sec. ANS: 48 rad 9. The angular acceleration ?, rad/s^2 of a rotating disk is related to its angular velocity ?, rad/s by ? = 4 √?. When t = 0, the disk is at rest and the angular position coordinate of a line in the disk is θ = 8rad. Find the expression for θ(?). ANS: θ(?) = 0.1667 ?^1.5 + 8 10. The rotation of a wheel is defined by the relation, θ = 3t^3 – 5t^2 + 7t – 2 where θ is in radian and t in seconds. Find the angular acceleration when t = 3 seconds. ANS: 44 rad/s^2 12. The shaft of a motor turns at constant speed of 3000 rpm. It turns to how many radians in 40 seconds. ANS: 12566.37 rad 13. The motor driving a grindstone is switched off when the latter has a rotational speed of 240 rpm. After 10sec, the speed is 180 rpm. If the angular retardation remains constant, how…

For the diagram below the angular velocity of the wheel is w = 2rad/s. The location of the instantaneous center of zero velocity is at point 0.3 m OD 1.2 m OB 45% O somewhere not listed in the other options. OC 0.3 m C

The figure as shown below is a rigid body undergoing planar motion. The absolute tangential accelerations of the points R and S on the body are 150 mm/sec2 and 300 mm/ sec2 respectively in the directions shown. What is the angular acceleration of the rigid body? Al 10 mm 10 mm 90 mm (a) 1.66 rad/ sec2 (b) 3.33 rad/ sec2 (c) 5.00 rad/ sec2 (d) 2.50 rad/ sec2 In the mechanism ABCD shown in the given figure, the fixed link is denoted as (1), Crank AB as (2), rocker BD as (3), Swivel trunnion at C as (4). The instantaneous centre I41 is at (a) the centre of swivel trunnion. (b) the intersection of line AB and a perpendicular to BD to (c) Infinity along AC (d) Infinity perpendicular to BD. www

A ball bearing is moving radially outward in a slotted horizontal disk that is rotating about the vertical z axis. At the instant shown in figure below, the ball bearing is 3.6 in from the center of the disk. It is traveling radially outward at a velocity of 4.4 in/sec relative to the disk and has a radial acceleration with respect to the disk of 5.3 in/sec? outward. What does the magnitude of 0 (in rad/s2) have to be for the ball bearing to have a total acceleration of zero? Figure is from "Engineering Mechanic An Introduction to Dynamics", McGill and King.

If a car is travelling along a straight road at 13.4 ms-1 and the linear speed of a point in the tyre is relative to the centre of the wheel making it 13.4 ms-1 too, and the radius of from the centre of the wheel to the tyre tread is 0.240 m, what is the angular speed of each tyre and what is the direction of the angular velocity vector of each wheel point in relation to the direction of the forward motion of the car?

A four-bar linkage is shown in the figure (the ground "link" OC is considered the fourth bar). If the angular velocity and angular A four-bar linkage is shown in the figure (the ground "link" OC is considered the fourth bar). If the angular velocity and angular acceleration of drive link OA are 6.1 rad/s and 6.6 ras/s^2 respectively, both counterclockwise, determine the angular accelerations of bars AB and BC for the instant represented. The angular accelerations are positive if counterclockwise, negative if clockwise. The answers are not: aAB= 2.356 and aBC = 11.327 or 390.82 and 465.7