Concept explainers
A wheel moves in the
Fig. P15.248
Velocity of point P at
Answer to Problem 15.248RP
The velocity at point P is equal to
Explanation of Solution
Given information:
Point P is located on horizontal diameter.
The angular displacement is given as:
The linear displacement is given as:
The angular velocity
The linear velocity
Calculation:
According to given information:
Differentiate
At
Therefore
Then
Differentiate
At
Therefore, the velocity of point P is:
Conclusion:
At
The velocity at point P is equal to
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics For Engineers
- A wheel moves in the xy plane in such a way that the location of its center is given by the equations xo=1213 and yo=R-2, where xo and yo are measured in feet and tis measured in seconds. The angular displacement of a radial line measured from a vertical where is measured in radians. Determine the velocity of the point Plocated on the horizontal diameter of reference line is 0-8 the wheel at f= 1.2 s R=2ft 6=81¹ Xo-12¹ The velocity of the point Pis ( ]/s)-([ ft/s)arrow_forwardAt the instant shown, the shaft and plate rotates with an angular velocity of 19 rad/s and angular acceleration of 9 rad/s². (Figure 1) Figure X D 0.4 m B 0 0.4 m a 0.3 m < 1 of 1 0.6 m 0.2 m C 0.3 m Part A Determine the velocity of point D located on the corner of the plate at this instant. Enter the x, y, and z components of the velocity in meters per second to three significant figures separated by commas. ► View Available Hint(s) (UD), (UD)y, (UD) z = 6.51,4.89,1.63 m/s Submit Previous Answers ✓ Correct Here we learn how to determine the velocity of a point on a rigid body revolving with an angular acceleration about a fixed axis in three dimensions. Part B Determine the acceleration of point D located on the corner of the plate at this instant. Enter the x, y, and z components of the acceleration in meters per second squared to three significant figures separated by commas. ► View Available Hint(s) (ap)z, (ap)y, (ap)₂ = [Π ΑΣΦ | ↓↑ vec Submit Previous Answers X Incorrect; Try…arrow_forwardDisk A rotates around the vertical z-axis with a constant angular velocity ω = dθ/dt = π/3 rad/s. At the same time, OB rotates around point O with a constant angular velocity dφ/dt = 2π/3 rad/s. At t=0, θ=0 and φ=0. The θ is the angle made with the fixed coordinate axis, the x-axis. A small sphere P slides down the rod according to the formula R=50+200t2, where R is in millimeters and t is in seconds. Calculate the magnitude of the total acceleration vector a of P at t=0.5 seconds.arrow_forward
- The crank link AB of the crank and slider mechanism has an angular velocity of WAB = 6 rad/s and an angular acceleration of a = 2 rad/s", both directed counterclockwise. The distances shown are hi = 6 in, h2 = 8 in and di 6 in. Also, a = 8, 6 = 15 %3D and c = 17. h2 WAB dAB What is the absolute value of the magnitude of the velocity of Point C at the given instant? vc =| in/s What is the absolute value of the linear acceleration of Point C at the given instant? in/s асarrow_forwardThe piston of the hydraulic cylinder gives pin A a constant velocity v = 2.4 ft/sec in the direction shown for an interval of its motion. For the instant when 0 = 59°, determine i, ř, 0, and Ö where r = OA. A. 5.3" Answers: ft/sec ft/sec? rad/sec = rad/sec2arrow_forwardThe crank AB has a constant angular velocity w. (Figure 1) Figure C (0) 1 of 1 X Part A Determine the velocity of the slider at C as a function of 0. Suggestion: Use the x coordinate to express the motion of C and the coordinate for СВ. Х = 0 when = 0°. Express your answer in terms of the variables b, 1, w, and 0. Enter the arguments of trigonometric functions in parenthesis. UC = Submit Part B - ΠΙΑΣΦΗ 11 ↓↑ ac = Request Answer Submit Determine the acceleration of the slider at C as a function of 0. Suggestion: Use the x coordinate to express the motion of C and the coordinate for CB. x = 0 when = 0°. vec Express your answer in terms of the variables b, 1, w, and 0. Enter the arguments of trigonometric functions in parenthesis. Enter the powers of trigonometric functions using parenthesis, e.g. (sin(0))³, (cos(0))4, etc. VE ΑΣΦ ↓↑ vec ? Request Answer ?arrow_forward
- For the disk rolling without slipping, if its radius r= 1.4 m, and its angular velocity W = 5.6 rad/s, determine the magnitude of the linear velocity of point B. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point and proper unit. В 45° No slipping Your Answer: Answer unitsarrow_forwardThe wheel in the figure rotates clockwise with a constant angular velocity of 120 rpm. The pin Dis fixed to the wheel at a point 125 mm from its center and slides along the guide in the arm AB. Determine: (a) The angular velocity AB (rad/s). b) The angular acceleration AB of the arm at the instant shown (rad/s2). 60 120 грm 375 mmarrow_forwardAB= 4 rad/s 45 125 mm B 300 mm Determine the angular velocity of the link CB at the instant shown on the linkage. AB is rotating at 4 rad/s. Angular Velocity of CB: से ९arrow_forward
- The r-y coordinate system is body fixed with respect to the bar. The angle 0 (in radians) is given as a function of time by 0 = 0.1+0.08t². The a coordinate of the sleeve A (in feet) is given as a function of time by x = 3+0.06t3. Determine the velocity of the sleeve at t = 4 s relative to a nonrotating reference frame with its origin at B. (Although you are determining the velocity of A relative to a nonrotating reference frame, your answer will be expressed in components in terms of the body-fixed reference frame.) (Figure 1) Enter the a and y components of the velocity separated by a comma. Πν ΑΣφ It vec ? VA 2, VA y = 2.88,4.92 ft/s Submit Previous Answers Request Answer X Incorrect; Try Again; 6 attempts remaining Figure < Return to Assignment Provide Feedback 1 of 1arrow_forwardQuestion 6 to this answer. At the instant shown, the bar AB has a velocity of 4.8 rad/s clockwise. If a = 0.22 m, b = 0.33 m,0 = 24°, and a = 52° at this instant. Determine the magnitude of the velocity in m/s of roller C. A 0 α Aarrow_forwardThe crank AB of the mechanism below rotates at 20 rad/s in the direction shown in the figure below. At the instant shown determine the velocity of point C.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