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A rotation is a curler movement of an object around a center of rotation. A 3-D object rotates around an imaginary line called a rotation axis. It this axis is within the body and passes through its center of mass the body will rotate upon itself or spin. A rotation about an external point is called a revolution when it is produced by gravity.

A rotation is a rigid body movement which is unlike a translation which keeps a point fixed. All rigid body movements are rotations, translation or combination of the two. A rotation is a progressive radial orientation to a common point. The distinction between a rotation and an orbit is the location of the axis of the rotation.

Rotations around the x, y, and z axes are called principal rotations. Rotations around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, followed by the rotation around the z axis.

The speed of rotation is given by angular frequency. The time-rate of change of angular frequency is angular acceleration. Said change is caused by torque. According to the right-hand rule, the direction away from the observer is associated with clockwise rotation and the direct towards the observer with counter-clockwise rotation.

A Horizontal Seismometer with a Pendulum

A horizontal seismometer consists of a pendulum of length "l" constrained to rotate about a nearly vertical axis. The angle away from vertical for the axis is "a" (alpha) and the mass is "m" a. Determine the Lagrangian for the system in terms of "theta", the angular displacement away from equilibrium about the axis. b. Find th

Rotations, reflections, translations for Diamond Structure

Please help with the following problems. The Bravais lattice of the diamond structure is fcc with two carbon atoms per primitive unit cell. If one of the two basis atoms is at (0,0,0), then the other is at (1/4,1/4,1/4). (a) Illustrate that a reflection through the (100) plane followed by a non-primitive translation thro

Inertia and Weighing Stop Signs

A shop sign weighing 245N is supported by a uniform 155N beam. Find the tension in the guy wire and the horizontal and vertical forces exerted by the hinge on the beam 708N, 580N, -6N The tires of a car make 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h. THE tires have a diameter of .90m a) What

Viscous Flow of Water in a Tank

See the attached file. We are presented with a 17000 gallon tank of water; the tank has specific dimensions and has a 75 horsepower agitator as noted and located in the attached file. The agitator is turning 385 rpm and the blades have a dimension of 42 inches tip to tip. We are asked to calculate the forces the rotating a

Newtonian Mechanics Problems Involving Rotation

1) The tub of a washer goes into its spin-drycycle, starting from rest and reaching an angular speed of 7.8 rev/s in 3.4 s . At this point the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 15.1 s . Through how many revolutions does the tub turn? Assume constant angula

Rotational Motion: Flywheel

A rim type flywheel has to store the greatest amount of energy of 2.5 kJ at the mean engine speed of 300 rpm. The fluctuation of speed is not allowed to exceed 1.5% of the mean and the mass of the flywheel is 500 kg. Assuming the flywheel to be of cast iron and having its internal diameter 0.9 of its external diameter, find the

Physics: Centrifugal force for glass and board swung on strings

A classic physics demonstration involves a glass of water placed in the middle of a flat board. If strings are then tied to the four corners of the board and the strings are swung rapidly in a vertical circle, the glass of water will remain in the center of the board as it spins and no water will spill out of the glass, even whe

Dynamics; Three problems

PROBLEM 1. When a car accelerates, the normal force at the tire/ground interface changes, increasing at the rear tires and decreasing at the front. Does the same occur for the Batmobile? The Batmobile is shown, along with its jet-engine propulsion system (please see the attachment). Assume an acceleration of 0.9g. Neglect grou

Kinetic Energy and Merry Go Round

See attached file. Please provide a stepwise solution. A merry-go-round of mass M=120kg and radius 5m rotates with an angular velocity ωo=3rad/s. A block of mass MA=90kg sits a distance RA=4m from the axis of rotation. At time t=0s, Bob (mB=70kg) jumps on the merry-go-round so that he lands a distance of RB=3m from the

Questions on Center of mass, Torque and Levers

Please refer to the attachment for the mentioned figures. 1. Three masses, 2.0 kg, 3.0 kg, and 6.0 kg, are located at points (3.0, 0), (6.0, 0), and (-4.0, 0), respectively, in meters from the origin. Where is the center of mass of this system? 2. A dumbbell, Figure below, has a connecting bar of negligible mass. Find the

Force and moment

1. Jane, a 120 lb woman, trips while walking down the street. She stumbles forward and falls onto her outstretched right hand. At the instant Jane's hand contacts the ground her whole body is moving downward at a velocity of 9 m/s and has a downward acceleration of 9.8 m/s2 (gravity). Her body rapidly decelerates after contac

Sound, Mass, Vector, Friction, Speed and Hooke's Law

1. According to a rule-of-thumb, every 3.0 seconds between a lightning flash and the following thunder gives the distance of the storm in km. Assuming that the flash of light arrives in essentially no time at all, estimate the speed of sound in kph from this rule. 2. A violent rainstorm dumps 1.0cm of rain on a city 4.4 km w

Frequency Coil Rotation

1. When its coil rotates at a frequency of 280hz, a certain generator has a peak emf of 75 V. a) What is the peak emf of the generator when its coil rotates at a frequency of 45 hz? b) Determine the frequency of the coils's rotation when the peak emf of the generator is 180V. 2. A series RCL circuit is a resonance and con

Rotation and torque

The L-shaped object in Figure 11-27 consists of three masses connected by light rods. See attached Figure. (a) What torque must be applied to this object to give it an angular acceleration of 1.27 rad/s2 if it is rotated about the x axis? _________N?m (b) What torque must be applied to this object to give it an angular acc

Angular Deceleration of a Centrifuge

A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off it continues to rotate with a constant angular deceleration fo

Laser: Interference and diffraction

Please solve and explain: A helium-neon laser provides coherent red light (wavelength < 1 &#956;m); the dimensions of the apertures or obstacles that we place in the laser beam are correspondingly small. A white sheet of paper attached with magnets to a screen mounted on one side panel of a lab bench. Laser set up at t

Centrifugal clutch

Please provide the solutions and answers to the attached questions. FIGURE 1 shows a centrifugal clutch. Each of the three equally spaced shoes with linings has a mass of 5 kg and is restrained radially by a tension spring as shown. For the stationary position shown, the residual tension in each spring is 200 N. Neglecting

Coriolis force and angular deviation of a Projectile

A projectile is fired horizontally along the earth's surface. Show that to a first approximation the angular deviation from the direction of fire resulting from the Coriolis force varies linearly with time at a rate of cos wq, where q is the angular frequency of the Earth's rotation and is the latitude angle, the direction of de

Equilibrium of Bodies: Force and Torque

If we have a uniform diving board, with a length 5.0 m and mass 54 kg, is supported at two points; one support is located 3.4 m from the end of the board and the second is at 4.6 m from the end (see the figure attached). What are the forces acting on the board due to the two supports when a diver of mass 65 kg stands at the end

Lagrange Multipliers and Forces of Constraint

With reference to Figure 2, a small cylinder sits initially on top of a large cylinder of radius a, the latter being attached rigidly to a table. The smaller cylinder has mass m and radius b. A small perturbation sets the small cylinder in motion, causing it to roll down the side of the large cylinder. Assume that the coefficien

Set of miscellaneous problems.

Chapter 11 : Conceptual Questions 8. Give two everyday examples of objects that are not in static equilibrium. 9. Give two everyday examples of objects that are in static equilibrium. Conceptual Exercise 4. Suppose the person in example 11-3 climbs higher on the ladder (please see the attachment for the fig).

Three problems on torque

Please help with the following physics problems. 1) A student pushes on a swinging door to leave a class. How much torque is exerted in each of the following cases if the force exerted is 50 N? A - The student pushes perpendicular to the door at the end farthest from the hinges (a distance of 80 cm). B - The student p

Scientific method : explained

Part 1 5. What must be your location if the stars move across the sky in circle centered directly overhead? 9. What is the basic difference between the Ptolemaic and Copernican models? Why the Ptolemaic model is considered incorrect? 10. Ancient astronomers were troubled by variations in the brightness of the various planets

Pressure in a Centrifuge

A test tube filled with liquid of uniform density rho, as shown in the figure (see attachment), is spun in a centrifuge with angular frequency w. The test tube lies perpendicular to the axis of rotation of the centrifuge. The pressure in the fluid at the distance r0 from the axis of rotation is p0. You may ignore the variation i

rotation, torque, and angular acceleration

Please see attachment. Thank You your help is greatly needed. 12. A top is spinning counterclockwise as shown in the figure. It is also moving to the right with a linear speed v. What is the direction of the angular velocity? 13. A wrench is used to tighten a nut as shown in the figure. A 12-N force is applied 7.0 cm from

angular velocity and angular acceleration

Could you please provide the answers and workings out to the following physics problems. 1. A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over 3.0-s interval. What is the angular acceleration of a point on the wheel? 2. During the spin-dry cycle of a washing machine, the motor slo