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Rotation

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

Minimum Value of Height Change

A uniform cylinder is allowed to roll down the track. Assume the cylinder rolls without slip, with r_1 = 1.0 m and R_2 = 0.04 m. What is the minimum value of h such that the cylinder never leaves the surface of the track? How would the height change if the object is a sphere? See the attached file.

Student's Angular Velocity

A uniform 25 kg disc with a diameter of 9 meters is mounted on a frictionless axle at its center. The disc is rotating at 2.2rad/s, up. A person (85kg) is initially at its center. The person then walks out to the edge of the disc, facing forward, and catches a 2.5kg ball tossed in his face at 18m/s with respect to the ground.

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

Pulley and Circle Dynamics

1. During poi (ball attached to the end of a piece of string) twirling demonstration the glowing ball comes off the string at the bottom of a vertical circle. a) Why was it more likely to come off at the bottom than at the top of the circle. b) If the length of the string is 60cm and it was being twirled so that it just got ov

A 15--diameter CD has a mass of 24 .

A 15--diameter CD has a mass of 24 . The CD's moment of inertia for rotation about a perpendicular axis through its center is =6.8 x 10^5 . What is the CD's moment of inertia for rotation about a perpendicular axis through the edge of the disk? Use 2 significant figures I = ______________________ kg.m^2

Rotational Motion of a Wheel

A wheel has a radius of 2.6 m. A. How far (path length) does a point on the circumference travel if the wheel is rotated through an angle of 51 degrees? Answer in units of m. B. How far (path length) does a point on the circumference travel if the wheel is rotated through an angle of 105 rad? Answer in units of m. C. Ho

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

Magnitudes and Angular Positions of Masses

See attached file for the graph. A rotating shaft carries three masses of A = 10 kg, B = 10 kg and C = 14 kg, their mass centres being 3, 4 and 5 cm respectively from the axis of rotation. The distance along the shaft between each mass is 0.4 m. The angles between the radii of A and B is 90° and between the radii of A an

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

Solving a Kinetic Energy Problem

An Atwood's machine consists of a disk of radius 19 cm and mass 2.5 kg, with masses of .5 kg and .65 kg suspended from a cord over the disk. If the cord does not slip on the disk, what is the total kinetic energy of this system when the masses are moving at 25 m/s?

Clock Pendulum and Mass Pivot Point

Please see the attached file for diagram. A designer wishes to make a clock with a pendulum in the shape of a flat disk. Instead of swinging from the end of a rod, however, the disk is to pivot about a point between its center of mass and its rim. If the disk has a radius of 15.0 cm and its intended period of oscillation

Solution for net torque

10.8.6. The corner of a rectangular piece of wood is attached to a rod that is free to rotate as shown. The length of the longer side of the rectangle is 4.0 m, which is twice the length of the shorter side. Two equal forces are applied to two of the corners with magnitudes of 22 N. What is the magnitude of the net torque and di

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

Determining rotation of a wheel and magnetic lines of bar magnets

1. A wheel is rotating at a rate of 2.0 revolutions every 3.0 s. Through what angle, in radians, does the wheel rotate in 1.0 s? , one revolution is the same as 2p radians. 2. Two identical bar magnets lie on a table along a straight line with opposite poles facing each other (the figure below (d)). Sketch the magnetic field

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

Rotation: tension and tangential velocity

** Please see the attached file for the complete solution response ** Please provide me step by step solution. A mass (M=3kg) is attached to a weightless cord of length L=2m is spun in a circular path. θ=85°. a) Draw the free body diagram for the mass at the point in time shown in the figure above. b) Wha

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

Linear Motion and Radial Acceleration of the Helecopter

Linear motion A model of a helicopter rotor has four blades, each of length 3.10 m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 490 rev/min. A) What is the linear speed of the blade tip? B) What is the radial acceleration of the blade tip expressed as a multiple

Sidereal and solar days

How and why does a day measured with respect to the Sun differ from a day measured with respect to the stars?

Mass and Average Density of Mars

Mars has two small satellites, Phobes and Deimos. Phobos circles Mars once every 0.31891 day at an average altitude of 5980 km above the planet's surface. The diameter of Mars is 6794 km. Using this information, calculate the mass and average density of Mars.