Problem 1A disk, mass 2kg, radius 0.5m spins at a constant angular speed w = 12s about an axlethat is at an angle 0 = π/6 to the normal to the disk. We choose our y-axis so that the axlelies in the xz-plane as shown below.wYou may use without proof that the moment of inertia of a disk around its center of mass isIo = MR² and about its diameter is ID = MR². All options are in SI units.(a) What is the angular velocity vector?(i) (6√√3,0,6)(ii) (6,0,-6√3)(iii) (6,0,6√3)(b) Using the Euler equations, find 7₁?(i) 0.(ii) -9√3/2.(iii) 9√3/2.(c) Using the Euler equations, find 72?(i) 0.(ii) -9√3/2.(iii) 9√3/2.

Answered: Image /qna-images/answer/1c949323-34f4-4c61-9e9b-ca3aa439d6bc.jpg

A disk, mass 2kg, radius 0.5m spins at a constant angular speed w = 12s¹ about an axle that is at an angle 0 = π/6 to the normal to the disk. We choose our y-axis so that the axle lies in the xz-plane as shown below.

A disk, mass 2kg, radius 0.5m spins at a constant angular speed w = 12s¹ about an axle that is at an angle 0 = π/6 to the normal to the disk. We choose our y-axis so that the axle lies in the xz-plane as shown below.

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 middle select menu is right or left.

A: The correct answers are calculated using Newton's second law.(b) m1 magnitude: 1.43 m/s2m1 direction…

Q: Q1) Pulley systems containing one, two, and three pulleys are shown. Neglecting the weights of the…

A: (a) One pulley(b) Two pulleys

Q: An L-R-C series circuit has L-0.600 H. C-8.00 μF. and R-350 Att-0 the current is zero and the…

A: the resistance R=350 ohmthe capacitance C=8 micro farad the inductance L=0.6 Hat t=0 charge is…

Q: Kyle, a 80.0 kg football player, leaps straight up into the air (with no horizontal velocity) to…

A: Solution Given dataMass of football player M=80kgMass of ball m=0.430kgDisplacement of player…

Q: A trough is filled with a liquid of density is 840 kg/m³. The ends of the trough are equilateral…

Q: 12. The racing car shown in the figure is traveling at 90 kph when it enters the semicircular curve…

Q: 1. A metal cylinder of radius a and length L has both ends held at a zero potential, and the sides…

A: uired

Q: 1. A 5-lb sphere is held in place on a semicircular hill with a radius of 12 ft. The sphere is…

Q: Is it always true that magnetic force and electric field are in the same direction? Also, why is -vB…

Q: Gas Pressure-the Atmospheric pressure - the particles of on objects. At high altitude, there is less…

A: Gas pressure-the Force exerted per unit surface area of an object.Atmospheric pressure - the…

Q: a) Define the reciprocal lattice vectors b1, b2, and b³ in terms of unit cell vectors a1, a2, and…

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

Q: Completed 30.00 20.00 10.00 0.08.00 P +20.00 +48.33 V PV Diagram for Isobaric 100.00 T +48.33 Volume…

Q: Check my work If 2.00 mol of nitrogen gas (N₂) are placed in a cubic box, 31.0 cm on each side, at…

A: Given,No of moles of N2 gas (n) = 200 molside of the cubic box (a) = 31 cmPressure (p) = 1.9 atm =…

Q: A one kilogram mass is dropped from a helicopter. Aside from the usual gravity, the other force is…

Q: The graph shows the x-directed force F, acting on an object as a function of the position x of the…

Q: There is a solid cylinder (radius R & mass M) at the top of a 4.2 m hill. What initial speed does…

Q: An 11 1/2 inch wide plank is cut in such a way that the width is in the tangential direction of the…

A: The objective of the question is to calculate the change in width of a wooden plank as the moisture…

Q: A block of unknown mass m is sliding down a smooth inclined plane. A physics student uses a motion…

A: From the figure above, we can see that the acceleration of a block down the inclined plane, making…

Q: 1. An electron moving in a conjugated bond framework can be viewed as a particle in a box. An…

A: Ans 1: (a) First order correction to the energy = 0.(b) The first order correction to the wave…

Q: 8. Capacitor consists of a sphere surrounded by a concentric spherical shell (R1=5cm, R2=15cm)…

Q: Two couples act on the frame. (Figure 1) Figure 100 lb 30% 13 ftd-3f1-B A ve 30⁰ 100 lb 150 lb 4 ft…

Q: Suppose a 443 g kookaburra (a large kingfisher bird) picks up a 74 g snake and raises it 2.3 m from…

A: Work done by a force to raise an object to a height is called the potential energy of the object

Q: John Acorn- Friday Fliers. Six, 8-foot (2.44 m) long aluminum “paper airplane” forms are placed…

Q: Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is…

Q: Power Calculation 1. A 50-kg marathon runner runs up the stairs to the top of the building at a…

Q: A Two 7.0 kg bodies, A and B, collide. The velocities before the collision are = (441+45) m/s and B…

A: We will answer the question using law of conservation of linear momentum. The detailed steps are…

Q: Problem 3: There are lots of examples of ideal gases in the universe, and they exist in many…

A: Please answer all parts:Problem 3: There are lots of examples of ideal gases in the universe, and…

Q: B. Determination of ₁ (accelerated motion)

A: The value of μk=0.0467 when the mass mb=130.15gThe value of μk=0.0448 when the mass mb+mwThe % of…

Q: Consider a 1.00 kg mass that is attached to a spring with spring constant 100.0 N/m and hangs…

Q: Q1: Compute linear density values for [100] and [111] directions for Silver and Iron.

Q: Exercise: Find the velocity ✓ of the particle as a function of r. Hint: 2 12 v = ŕŕ + rėê r = ± (E-…

Q: 1. A metal cylinder of radius a and length L has both ends held at a zero potential, and the sides…

Q: PRACTICE IT Use the worked example above to help you solve this problem. Consider a capacitor C…

Q: Why is the following situation impossible? A laser beam strikes one end of a slab of material of…

Q: A spin-2 system has 5 spin states in the Sz basis. Express the following as matrices or vectors in…

A: Let us consider the spin 2 system with 5 spins.The total spin angular momentum quantum no, S =…

Q: A particle with mass m is moving in one dimension in the potential V(x). The particle is in a state…

A: For a particle of mass m moving in one dimension in the potential V(x), the hamiltonian or energy…

Q: The classical turning points of a harmonic oscillator occur at the displacements at which all of the…

A: The energy of the oscillatoe for state ν=0 is given byNow equating this energy with potential…

Q: Q3. A monochromatic X-rays beam is used for a dental exam. Which material would you choose for an…

A: GivenA monochromatic X-ray beam is used for a dental exam. Which material would you choose for an…

Q: LASICISe Disk A, of weight 10 lb and radius r = 6 in., is at rest when it is placed in contact with…

Q: The river flows north at 4 m/s as given in Figure 3. Assume that the current is uniform. If one…

Q: A person walks first at a constant speed of 4.80 m/s along a straight line from point to point B and…

A: Average velocity is defined as, ratio of total distance travelled over total time.where

Q: in the figure by using vector addition. (Assume that the +x-axis is to the right and the +y-axis is…

Q: rticle confined to a 1-dimensional box of

Q: Use the following half-life graph to answer the question: What is the mass of the radioactive…

Q: Neil and Gus are having a competition to see who can launch a marble highest in the air using a…

Q: The velocity field in a potential flow is governed by the two kinematic equations grad*u=0 and…

A: The velocity field in a potential flow is governed by the two kinematic equations grad*u=0 and…

Q: We can represent the Hadamard gate in Sz basis, as shown in the attached image. Show that the…

Q: An object is dropped from a tower, 1024 ft above the ground. The object's height above the ground t…

Q: Two black flies are sitting 7.52 cm apart on a hamburger bun on a picnic table. A spy satellite with…

Q: 12. A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the…

A: Given data: -x1i=5 m/sxif=4.33 cos30∘m+Vsinθ mθ1=30∘Find: -The struck ball's velocity.

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

Problem 1
A disk, mass 2kg, radius 0.5m spins at a constant angular speed w = 12s about an axle
that is at an angle 0 = π/6 to the normal to the disk. We choose our y-axis so that the axle
lies in the xz-plane as shown below.
w
You may use without proof that the moment of inertia of a disk around its center of mass is
Io = MR² and about its diameter is ID = MR². All options are in SI units.
(a) What is the angular velocity vector?
(i) (6√√3,0,6)
(ii) (6,0,-6√3)
(iii) (6,0,6√3)
(b) Using the Euler equations, find 7₁?
(i) 0.
(ii) -9√3/2.
(iii) 9√3/2.
(c) Using the Euler equations, find 72?
(i) 0.
(ii) -9√3/2.
(iii) 9√3/2.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Write the given data with suitable variables-

VIEW

Step 2: Determine the value of each variables-

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 6 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

Example 3-3: Parallel-Axis theorem and composite bodies A clock pendulum consists of a slender rod and a circular disc with a hole in it as shown. The rod 20 cm has a density of 7000 kg/m3 and cross sectional area of 50 mm2 he disc has a density of 8000 kg/m3 and a thickness of 5 mm. 5 ст 10 ст Compute the moment of inertia of the pendulum about O.
A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car The combined moment of inertia of the rotating masses is 10 kg-m².what is the magnitude of the gyroscopic moment in (N-m)?
Two thin hoops of masses m1 and m2 have radii a1 and a2, respectively. They are mounted rigidly on a frame of negligible mass. Find the systems moment of inertia about an axis through the center and perpendicular to the page. How large a torque must be applied to the system to give it an angular acceleration α about this axis, provided it is free to turn? Repeat tor the axis AA’.
| Link BC has a mass mgc = 4 kg, with a moment of inertia about its mass center of: laac = maclic Link AB has a mass mAR = 2.4 kg, with a moment of inertia about point A of: The wheel at point C is of negligible mass. At the moment pictured below, the velocity of point C is 1.5 m/s to the right. Find the velocity of pin B after link AB has rotated through 90°.
Gravitational acceleration g = 10 m/s? 1. A uniform thin rod of length Im and mass m,od = 20 Kg in the figure can rotate freely in the plane about an axis at 30 cm from one of its ends while the other end attached with a disk of radius 10 cm and mass maisk = 10 Kg. As the rod swings from the angle 30". a. Find the position center of mass. b. Calculate the moment of inertia for the composed system. c. What is the velocity of the disk while reaching an equilibrium point? 30 cm
Match the most appropriate form of the equation for the moment of inertia to the image shown. All objects are rotating about point O. Note: ris distance, m is a mass, k is a radius of gyration and d is a distance from the mass moment of inertia IG about the center of mass A. D. O M X Mass element Z Rotation axis X A.1=1+md² G B. = SM √² r²dm C.I=mk²_ D.1= Σm,r?
5kg plate, and 3 kg slender rod. FIND, the radius of gyration of the pendulum about an axis perpendicular to the screen and passing through the point G.
Slender rod with mass of 2 kg. and cicular plate with mass of 4 kg. FIND, the pendulum radius of gyration about an axis perpendicular to the screen passing through point O
A wheel is attached by a cable to a block The wheel has a radius of 2ft and weighs 300lbs, the block weights 20lbs. If the radius of gyration about the point of rotation of the disk is 1.5ft, how many revolutions will it take for the wheel to come to a stop assuming it was moving at 10 rad/s CW. Assume the block is on the left side of the wheel and thus causes a CCW moment.
The crankshaft of a vertical sıngle-cylinder engine, stroke 250 mm, rotates at 300 r/min The reciprocating parts ( including part of the connecting rod) have a mass of 100kg The connecting rod has a mass of 120 kg, it is 450 mm long, the centre of mass is 300 mm from the gudgeon pin axıs and the radiųs of gyration about the same axıs is 363 mm When the crank is 30° from the t dc position and moving downwards, determine 31 the side thrust on the cylınder walls due to the inertia of the reciprocatıng parts, and 32 the crankshaft torque on the crankshaft due to inertia
Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt. mass1=10kg Jo=20kg-m2 mass2=15kg, a is half of b. The rocker is 30 centimeters long. (kg-m2) * k1 Jo- k2 m2
Examples: Moments of inertia of the pendulum about an axis 1) passing through point O, and 2) mass center G of the pendulum. Both rods OA and BC are uniform. Rod OA weighs 10 lb, and BC weighs 8 lb. B A y 2 ft 1 ft1 ft C