Concept explainers
A wheel moves in the xy plane in such a way that the location of its center is given by the equations xO = 12t3 and yO = R = 2, where xO and yO are measured in feet and t is measured in seconds. The angular displacement of a radial line measured from a vertical reference line is θ = 8t4, where θ is measured in radians. Determine the velocity of point P located on the horizontal diameter of the wheel at t = 1 s.
Fig. P15.248
Find the velocity of the point P located on the horizontal diameter at time
Answer to Problem 15.248RP
The velocity of the point P located on the horizontal diameter at time
Explanation of Solution
Given information:
Show the location of the center of the wheel as follows:
Here,
The angular displacement of the radial line measured from vertical reference line is denoted by
Show the angular displacement
Here,
Calculation:
Consider the position of the point P with respect to point O is denoted by
Calculate the angular velocity of the wheel at time
Substitute
Substitute
Calculate the velocity at point O using the relation:
Substitute
Substitute
Show the relation between the velocity at point P and O as follows:
Substitute
Thus, the velocity of the point P located on the horizontal diameter at time
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- Disk 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_forwardThe 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 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_forward
- The ladder of the fire truck rotates around the z axis with an angular velocity of w₁ = 0.12 rad/s, which is increasing at 0.24 rad/s². At the same instant it is rotating upwards at w₂ = 0.56 rad/s while increasing at 0.44 rad/s². (Figure 1) Figure a 40 ft 30° 1 of 1 Part A Determine the velocity of point A located at the top of the ladder at this instant. Enter the components of the velocity in feet per second to three significant figures separated by commas. VAZ, VAy, VAz = Submit Request Answer Part B ■A£¢↓↑vec Az Ay, Az = Determine the acceleration of point A located at the top of the ladder at this instant. Enter the components of the acceleration in feet per second squared to three significant figures separated by commas. 15] ΑΣΦΗ ? vec ft/s ? ft/s²arrow_forwardThe disk rotates about the shaft S, while the shaft is turning about the z axis at a rate of w₂ = 6 rad/s, which is increasing at a = 2.5 rad/s². No slipping occurs. (Figure 1) Figure B 0.1 m S tiff 83 0.5 m 0.1 m 1 of 1 Part A Determine the x, y, and z components of the velocity of point B on the disk at the instant shown using scalar notation. Express your answers using three significant figures separated by commas. (VB)z, (UB)y, (UB)₂ = (0,6,0) Submit 17 ΑΣΦ ↓↑ Part B Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining (aв)z, (aв)y, (aB)₂ = vec Submit Request Answer Determine the x, y, and z components of the acceleration of point B on the disk at the instant shown using scalar notation. Express your answers using three significant figures separated by commas. ? A vec m/s ? m/s²arrow_forwardFor 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_forward
- Member AB is rotating at a constant speed of 4 rad/sec as shown. Find the angular velocity of bar BC at the instant shown. What is velocity of the point D at the center of bar BC? Bar BC is 3 ft in length. 20° 45% Xarrow_forwardThe crane boom OA rotates about the z axis with a constant angular velocity of w₁ = 0.18 rad/s, while it is rotating downward with a constant angular velocity of w₂ = 0.7 rad/s. (Figure 1) Figure 50 ft 601 110 C ▾ Part A ▾ Determine the velocity of point A located at the end of the boom at the instant shown. Enter the components of the velocity in feet per second to three significant figures separated by commas. Submit Part B a₁ = IVE] ΑΣΦΗ Π Submit AΣ vec Request Answer Determine the acceleration of point A located at the end of the boom at the instant shown. Enter the components of the acceleration in feet per second squared to three significant figures separated by commas. ■■■VA£¢ 1 vec 151ΑΣΦΗ Provide Feedback Request Answer ? 3 → Ⓒ ft/s ? ft/s²arrow_forwardFor the mechanism in the image below, the end A of the bar is moving downward along the slotted guide with a constant velocity VA = 2.0 m/s. If r = 0.5 m, determine the angular velocity W of bar AB when 0 = 49°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point and proper unit. A W, a у В Your Answer: Answer unitsarrow_forward
- For the mechanism in the image below, the end A of the bar is moving downward along the slotted guide with a constant velocity VA = 1.7 m/s. If r = 0.5 m, determine the angular velocity W of bar AB when = 34° . Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point and proper unit. B Your Answer: Answer ω, α units A 0 A yarrow_forwardThe electric fan is mounted on a swivel support such that the fan rotates about the z axis at a constant rate of w₂ = 1 rad/s and the fan blade is spinning at a constant rate wę = 54 rad/s. 6 = 45° for the motion. (Figure 1) Figure W: @₂ 1 of 1 Part A Determine the x, y, and z components of the angular velocity of the blade using scalar notation. Express your answers in radians per second to three significant figures separated by commas. (w) x, (w)y, (w) x = Submit Request Answer Part B (a)x, (a)y, (a)₂ = Submit Provide Feedback ΑΣΦ Determine the x, y, and z components of the angular acceleration of the blade using scalar notation. Express your answers in radians per second squared to three significant figures separated by commas. V— ΑΣΦ Request Answer vec ↓↑ vec ? M rad/s ? rad/s² Next >arrow_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_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