Concept explainers
The disk shown moves in the xy plane. Knowing that (vA)y = −7 m/s, (vB)x = −7.4 m/s, and (vC)x = −1.4 m/s, detemine (a) the velocity of point O, (b) the point of the disk with zero velocity.
Fig. P15.44 and P15.45
(a)
Find the angular velocity of point O.
Answer to Problem 15.45P
The angular velocity of point O is
Explanation of Solution
Given information:
Show the velocity
Consider the velocity of point C and B with respect to A is denoted by
Consider the position of point C, B, O with respect to A is denoted by
Calculation:
Show the position
Calculate the velocity
Substitute
Show the components of i on both sides of the Equation (1).
Show the components of j on both sides of the Equation (1).
Calculate the velocity
Substitute
Show the components of the i on both sides of the Equation (4).
Show the components of the j on both sides of the Equation (4).
Refer Equation (2).
Substitute
Calculate the velocity
Substitute
Consider the velocity at the point O is denoted by
Consider the velocity of the point O with respect to A is denoted by
Calculate the velocity of the point O using the relation:
Substitute
Thus, the velocity of the point O is
(b)
Find the point in the disk with zero velocity.
Answer to Problem 15.45P
The point on the disk with zero velocity is
Explanation of Solution
Given information:
Calculation:
Consider the point on the disk with zero velocity is
Show the distance
The velocity
Show the velocity
Substitute 0 for
Equate i component on both sides of the Equation (7).
Equate j component on both sides of the Equation (7).
Thus, the point with zero velocity is
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- In order to uncoil electrical wire from a 0.6-m-radius spool fixed to a truck, a worker drives to the left with a speed of vA = 5 m/s. At the same time, a second worker holds the cable as he walks to the right with a speed of vB = 3 m/s. Knowing that at the instant shown the thickness of wire on the spool is 40 mm, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the inside of the spool.arrow_forwardThe disk shown moves in the xy plane. Knowing that (vA)y = −7 m/s, (vB)x = −7.4 m/s, and (vC)x = −1.4 m/s, determine (a) the angular velocity of the disk, (b) the velocity of point B.arrow_forwardIn order to uncoil electrical wire from a spool fixed to a truck, a worker drives to the left with a speed of vA = 4 m/s. At the same time, a second worker holds the cable as he walks to the right. Knowing that at the instant shown the thickness of wire on the spool is 50 mm and that the 0.6-m-radius spool has an angular velocity of 8 rad/s, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the spool, (c) the speed of the second worker B.arrow_forward
- In Prob. 15.14, determine the velocity and acceleration of point E , assuming that the angular velocity is 26 rad/s and increases at the rate of 65 rad/s2.Reference to Problem 15.14:A circular plate of 120-mm radius is supported by two bearings A and B as shown. The plate rotates about the rod joining A and B with a constant angular velocity of 26 rad/s. Knowing that, at the instant considered, the velocity of point C is directed to the right, determine the velocity and acceleration of point E.arrow_forwardA helicopter moves horizontally in the x direction at a speed of 120 mi/h. Knowing that the main blades rotate clockwise when viewed from above with an angular velocity of 180 rpm, determine the instantaneous axis of rotation of the main blades.arrow_forwardIn the simplified sketch of a ball bearing shown, the diameter of the inner race A is 60 mm and the diameter of each ball is 12 mm. The outer race B is stationary, while the inner race has an angular velocity of 3600 rpm. Determine (a) the speed of the center of each ball, (b) the angular velocity of each ball, (c) the number of times per minute each ball describes a complete circle.arrow_forward
- Knowing that at the instant shown the angular velocity of rod DE is 15 rad/s clockwise, write down the equation of velocity of point D relative to point E.arrow_forwardA painter is half way up a 10-m ladder when the bottom starts sliding out from under him. Knowing that point A has a velocity vA = 2 m/s directed to the left when 0= 60°, determine (a) the angular velocity of the ladder, (b) the velocity of the painter.arrow_forwardIn a four bar mechanism, the dimensions of the links are given as AB = 50 mm, BC = 66 mm, CD = 56 mm and AD = 100 mm. At a given instant when <DAB=600 . The angular velocity of link AB is 10.5r/s in CCW direction. Determine, (i) velocity of point C, (ii) velocity of point E on link BC when BE = 40 mm, (iii) the angular velocity of link BC and CD; (iv) the velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. (v) the velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise (arrow_forward
- Problem 1: In a four bar mechanism, the dimensions of the links are as given below: AB = 50 mm, BC = 66 mm CD = 56 mm and AD = 100 mm At a given instant when |DAB 60o the angular velocity of link AB is 10.5 r/s in CCW direction. Determine, i) Velocity of point C ii) Velocity of point E on link BC when BE = 40 mm iii) The angular velocity of link BC and CD iv) The velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. v) The velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise. vi) The velocity of rubbing of pins A, B, C and D. The ratio of the pins are 30 mm, 40 mm, 25 mm and 35 mm respectively.arrow_forwardIn a four-link mechanism, the dimensions of the links are given as AB=50mm, BC=66mm, CD=56mm, and AD=100mm. At the instant when <DAB = 60° , the link AB has an angular velocity of 10.5 rad/sec in the counterclockwise direction. Both A and D lies in the horizontal plane.For the given configuration of the mechanism, determine the following: angular velocity of the link CD, angular velocity of the link BC, velocity of an offset point G on the link CD if CG=24mm,DG=44mm Instructions: configuration diagram Scale: 1:1 velocity diagram. Scale: 1m/s : 95mmarrow_forwardAt the instant shown, the velocity of collar A is 0.4 m/s to the right and the velocity of collar B is 1 m/s to the left. Determine (a) the angular velocity of bar AD, (b) the angular velocity of bar BD, (c) the velocity of point D.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY