The T shaped plate is rotating at a rate of w = 10 rad/s CCW (as shown) and deccelerating at a rate of a = -2.5 rad/s². The relevant dimensions of the plate are a = 3 in and b = 2 in. The plate is inclined at an angle = 15 deg at the instant shown. 1. What are the inertial velocity and acceleration vectors of points P and Q in terms of the unit vectors b₁ and b₂? 2. Which point has a greater velocity magnitude? acceleration magnitude? 3. How much of the acceleration is due to the Coriolis effect? 4. How many revolutions will the plate complete before reaching zero angular velocity? 23 a P b₂ b b3 Q b₁ a

The T shaped plate is rotating at a rate of w = 10 rad/s CCW (as shown) and deccelerating at a rate of a = -2.5 rad/s². The relevant dimensions of the plate are a = 3 in and b = 2 in. The plate is inclined at an angle = 15 deg at the instant shown. 1. What are the inertial velocity and acceleration vectors of points P and Q in terms of the unit vectors b₁ and b₂? 2. Which point has a greater velocity magnitude? acceleration magnitude? 3. How much of the acceleration is due to the Coriolis effect? 4. How many revolutions will the plate complete before reaching zero angular velocity? 23 a P b₂ b b3 Q b₁ a

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: The velocity of a boat relative to a fixed-earth coordinate system is 12 m/s and is constant. The…

A: Given: Speed of the boat→Vb=12 m/s Length of the tow rope→L=15 m Initial angle→θ=30° Rate of…

Q: Can someone solve and explaine this mechanics problem? For the mechanism shown in the figure v1 =…

Q: The disk rotates about the shaft S, while the shaft is turning about the z axis at a rate of w₂ = 6…

A: To Find : The component x,y and z of velocity at point B The component x,y and z of acceleration at…

Q: 3) Link AB of a robotic arm is rotating at a constant speed of 4 rad/s, while link BC is rotating at…

Q: The disk with radius r = 0.2 m (figure below) starts from rest and receives an angular acceleration…

Q: A load is raised 11 ft by the gears and wheel system below. Gear A is initially rotating at rest and…

Q: 5. For the following pin-collected link assembly, link AO is pinned at point O, and moves with…

Q: 1. A pancake body rotates about a fixed origin. Relative to that origin, a point A at A = az on the…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: A spool with an outer diameter of 8 cm descends by unwrapping an inextensible cable that is wound…

Q: Figure 7 illustrates a rotational bracket system. Originally, the bracket rotates about the shaft O…

Q: 5. For the following pin-collected link assembly, link AO is pinned at point O, and moves with…

Q: A ball bearing is moving radially outward in a slotted horizontal disk that is rotating about the…

A: Given: r=3.6 inr˙=4.4 in/sr¨=5.3 in/s2 Find: What does the magnitude of θ¨have to be for the ball…

Q: 3. The bar shown rotates about the z-axis. Find the velocity and accleration of point P for the…

A: Given: Angular acceleration of the bar: →α=4 rad/s2 (clockwise) Angular velocity of the bar:…

Q: A circular saw blade 0.6 m in diameter starts from rest and accelerates with constant acceleration…

A: To get the required solution to the above equation, we will use the equation of motion which is…

Q: The platform in figure is rotating with a constant angular velocity of w = 0.2 rad/s. Pivoting on…

A: Write the angular velocity of the particle. ωt=dθdt=π62cos2t=π3cos2t

Q: Question 1) the scalar magnitude of the velocity at time 2.0512 second Question 2) the scalar…

A: 1) To calculate the scalar magnitude of the velocity at time 2.1407" data-mce-style="display:…

Q: B. Vrel, Arel OBC ABC 1.25 m 0.25 m 30 ° A Figure 2 Disk BC totates in counterclockwine direction as…

Q: 5. For the following pin-collected link assembly, link AO is pinned at point O, and moves with…

Q: A motor winds the pulley at A with the kinematic quantities given. Find the acceleration of block E…

A: Given: To find: Acceleration of block E

Q: A basketball player attempts a three-point shot 10.0 m from the basket as shown in the figure below.…

A: The components of the initial velocity are Vx = Vcos38.8o and Vy = Vsin38.8o the time for the ball…

Q: The reference frame below is rotating with a constant angular velocity of 8,7k rad/s while point A…

A: Write the expression for the angular acceleration. Here, v represents the velocity of point A and ω…

Q: A model car is moving on a circular track of radius r = 208m₁ (in degrees) given by the formula…

Q: 1)Write the time derivative of the usual basis vectors in polar coordinates in terms of ø . Use…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A wagon is moving in a straight line with constant acceleration az and its kinematics is measured…

A: In X-direction, the acceleration is Fx is the force in x-direction abx=FxM-ax

Q: (Use relative motion analysis): The planetary gear system is used in car transmissions. There is sun…

Q: The crank rod (OB) in the crank-piston mechanism shown in the figure is rotating with CONSTANT n rpm…

A: Slider crank mechanism Slider crank mechanism is used to transfer angular motion of the crank to…

Q: To calculate the angular speeds of the two bars B2 and B3, you need to use the two point formula:

Q: Curvilinear Motion: Cylindrical Components 7 of 12 Three stock car drivers are racing around a…

Q: = 6 m, For the system displayed in the figure below, the lengths of rigid-body OA and AB are l₁ 1₂ =…

A: The values are l1=6 m, l2=4 m, θ=65°,ψ=68°, h=1.5 m The velocity of roller B is Vb⇀=5.5i⇀ m/s The…

Q: 6. In the linkage below, the angular velocity of link 2 is 100 rad/s CCW. The linkage dimensions are…

A: The Answer is Below

Q: A flywheel is mounted with a fixed axis of rotation through 0, a constant as shown. It starts at…

Q: 5. For the following pin-collected link assembly, link AO is pinned at point O, and moves with…

A: Write the given data. ω=5.4 rad/sα=7.8 rad/s2l=2.1 mθ=30°

Q: Q2: The boat in Fig.2 is traveling at 40km/h. The rope to tow the parasail is 150m long. At the…

Q: Unlike the common V6 engine, Subaru engines contain pistons that are horizontally opposed (see…

A: Given: The angular speed of AB, wAB = 2000 rpm The angle, θ = 40° The length of bar AB, r1 = 3 in…

Q: VC= UB 11 B Vmax= m/s m/s Ꮎ = 15 cm wheel pictured above is rolling while slipping. If the center of…

Q: Consider the mechanism shown. Members PQ and QR are joined by a hinge at Q. End P of member PQ is…

Q: A shaft 5.0 cm in diameter and rotating at 2,400 rpm, comes to a full stop in 6.0 seconds. It slows…

Q: 2 = 2.3 ft, VA = 4.7 ft/s, aa = 2.7 ft/s2, and the a cceleration (in rad/s2) of rod ABC. Negative…

A: l1=1.1ftl2=2.3ftvA=4.7ft/saA=2.7ft/s2θ=25° To-Find:- Angular acceleration=?

Q: For the linkage shown in the figure, using the graphyical velocity analysis method find the angular…

A: For the linkage shown in the figure, using the graphyical velocity analysis method. find the angular…

Q: . Consider the conveyor belt shown below. As the rollers turn at a constant rate, the top portion of…

Q: 4. A weight, attached to a cord, is travelling on a smooth circular table. A cord is pulling the…

A: The given data with the suitable variables is shown below. vr=5 cm/sθ˙=10 rad/saθ=0r=20 cm

Q: In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it.…

A: Note: As per our guidelines we are supposed to answer only the first 3 sub-parts. Kindly repost…

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

100%

The T shaped plate is rotating at a rate of w = 10 rad/s CCW (as shown) and deccelerating at
a rate of a = -2.5 rad/s². The relevant dimensions of the plate are a = 3 in and b = 2 in. The
plate is inclined at an angle = 15 deg at the instant shown.
1. What are the inertial velocity and acceleration vectors of points P and Q in terms of the
unit vectors 6₁ and 6₂?
2. Which point has a greater velocity magnitude? acceleration magnitude?
3. How much of the acceleration is due to the Coriolis effect?
4. How many revolutions will the plate complete before reaching zero angular velocity?
iz
a
b₂
9
.........
b
Q
a

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Determine the inertial velocity and acceleration vectors of point P and Q.

VIEW

Step 2: Calculate the inertial velocity and acceleration vectors of point P and Q.

VIEW

Step 3: Explain which point has greater velocity and magnitude.

VIEW

Step 4: Calculate the number of revolution before reaching zero angular velocity.

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 19 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Consider a circular disc which is rotating about its geometric center with a circular motion such that the angular acceleration is a quadratic function in time such that the time derivative of the angular acceleration is proportional to the time. For a particular angular acceleration motion at a time of t₁ = 0.1047 second the angular acceleration is a₁ =-0.1568 meter per second squared and at a time of t2=0.514 second the angular acceleration is a2 =0.9995 meter per second squared. At a time of t3=1.1999 second the angular velocity is w=9.9219 radians per second. Calculate the following at time t4=2.2023 second and a point on the disc where the radius is r=0.6351 meter: Question 1) the scalar magnitude of the velocity at time 2.2023 second Question 2) the scalar magnitude of the normal component of the vector of the acceleration at time 2.2023 second Question 3) the scalar magnitude of the tangential component of the vector of the acceleration at time 2.2023 second
For the disk rolling without slipping, if its radius r = 2.0 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. B Your Answer: Answer 45° r No slipping units
The 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 >
A motorcycle cage has a curved path in the x-z plane as shown. The cage path has different curved profile, and between point o and A the path is best described as z = f(x) = ax², where a = 0.09 and b = 1.23. The motorcyclist at point M is moving at a velocity of 12.6 m/s which is increasing at a rate of 1.9 m/s?. If the horizontal position of the motorcyclist at point M is xM = 11.9 m, determine (i) the direction of the motorcyclisť's velocity. (ii) the radius of the curvature of the cage's path at point M, (iii) the normal acceleration at point M, (iv) the magnitude and direction of the motorcyclist's acceleration at point M. A (z = ax
Rod OA rotates counterclockwise with a constant angular velocity of 0 = 5 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other slides over the horizontal curved rod, of which the shape is described by the equation = 1.5(2-cos) ft. (Figure 1) Figure r = 1.5 (2 cos 6) ft 6 = 5 rad/s 1 of 1 Part A If both collars weigh 0.60 lb, determine the magnitude of the normal force which the curved rod exerts on one collar at the instant = 140 °. Neglect friction. Express your answer to three significant figures and include the appropriate units. N = Submit μA Value Request Answer Units < Return to Assignment Provide Feedback ?
The known angular velocity of link AB is wAB and the unknown angular velocity of link BC is wBc. Determine the velocity vectors V B, V C, and w BC using a relative motion analysis. Reduce/simplify all expressions as far as possible. The only parameters that should appear in your symbolic solution include wAB, LAB, LBc, 0, and ø. Finally, numerically evaluate the three velocity vectors using values LAB = 2 m, LBC 1.5 m, WAB = 0.25 rad/s, 0 = 30°, and ø = 10°. В LBC LAB W BC WAB
+ G In the above diagram, the wheel starts from rest and rolls without slipping. The force (you don't need the value) causes a constant angular acceleration of 7.112 rad/s2. The radius of the wheel is R - 0.392 m. What is the magnitude of the acceleration of the point at the top of the wheel at time t 1.400 s? This is the point at the outer edge directly above the center of gravity, Gwhere the force F connects to the wheel. Use units of m/s. Don't place units in your answer, 3 o
A cylinder of radius 7 = 0.2 m is about to start rolling down an inclined plane. The acceleration of the center of the cylinder is 9.81 sin(0) m/s?. The angular acceleration is 9.81 sin(0)/r rad/s?. Assume 0 = 0.8 rad. What is the magnitude of acceleration of the point on the cylinder furthest from the inclined plane in m/s?. Hint: Since it is about to start rolling, the velocity of the center of the cylinder and angular velocity of the cylinder are still zero at that instant. You Answered 0.2739 Correct Answer 14.075 margin of error +/- 2%
Advanced Applied Mathematics - Circular Motion 1. When an airplane touches down at 1 = 0, a stationary wheel is subjected to a constant angu- lar acceleration a = 110 rad/s until / = 1 s. (a) What is the wheel's angular velocity at t = 1 s? (b) At 1 = 0, the angle 0 = 0. Determine 9 in radians and in revolutions at / = 1 s. 2. A small box B of mass mkg is placed on a rough horizontal rotating disc. B is metres from the centre of rotation as shown in Fig. 1 below. The coefficient of friction between the disc and B is u. Find, in terms of u, r and g, the maximum speed v that can be given to B without it slipping. 3. One end of a light inextensible string of length L metres is attached to a fixed point C. A small brass hall Ro
The in-plane angular speed of the bent bar indicated below is w = 0.2 rad/s. The dimensions of the bar are L = 0.4 m and H = 0.6 m. Find the magnitude of the velocity (in m/s) of the endpoint B. H B L Figure is from "Engineering Mechanic An Introduction to Dynamics", McGill and King.
-10 10 40 a. Find the volume of the parallelepiped whose edges are represented by A = 2i - 3j + 4k, ii. B = 1+ 2) - k, C = 31 - 1 + 2k . b. The angular velocity of a rotating rigid body about an axis of rotation is given by ai = 4i +j - 2k. Find the linear velocity of a point P on the body whose position vector relative to a point on the axis of rotation is 2i-3j+k. ii. Find the moment of inertia tensor from the given picture. 300 mm P.T.O. iv. Given point P = (1, -2, 3) and vector A = yz i+x1- yx k , express this vector in cylindrical coordinate system. V. a. Show that the contraction of the outer product of the tensors AP and B, is an invariant. b. Show that every tensor can be expressed as the sum of two tensors, one of which is symmetric and the other skew-symmetric in a pair of covariant or contra variant indices. vi. The 4-oz top with radius of gyration about its spin axis of 0.62 in. is spinning at the rate p = 3600 rev/min in the sense shown, with its spin axis making an angle…