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# Rotation

### Determining Distance: Plank Example Question

How far out the plank can a 50kg object be placed before the plank tips? The mass of the plank is 400kg, its length is 10 m, and it has supports from below at the center and 1m from the same end as the object is nearest.

### Magnetic Moment of a rotating charged sphere.

Given the radius of a proton is approximately 1x10^-15m, assume that it is a rotating, uniformly charged sphere with a magnetic moment of 4.5x10^-26 J/T. a) First demonstrate that J/T is equivalent to Am^2 b) What is the approximate angular frequency of the proton?

### 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

### Physics: linear vs rotational speed, bicycle speed, rotational inertia, gyroscope, force

1. Explain the difference between linear speed and rotational speed. Include formula difference and how rotational speed is changed to linear speed. 2. A bicycle has wheels with a 30-centimeter radius. If smaller wheels with a 25-centimeter radius are installed, what is the change in linear speed of the bicycle if the wheels

### Physics - Angular Speed of Rotation

In an amusement park rocket ride, cars are suspended from L = 4.17-m cables attached to rotating arms at a distance of d = 6.15 m from the axis of rotation. The cables swing out at an angle of _ = 46.2_ when the ride is operating. What is the angular speed of rotation? (File is attached below)

### 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

### Center of Mass and Magnitude of Force

A 64.0 kg person stands on a lightweight diving board supported by two pillars, one at the end of the board, the other 1.20 m away from the end. The pillar at the end of the board exerts a downward force of 837 N. (a) How far from the pillar at the end of the board is the person standing? (b) Find the magnitude of the force

### 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

### Moment of inertia tensor

Find the tensor of inertia about the center of mass of a flat rigid body in the shape of 45 degrees right triangle with uniform mass density. What are the principal axes. What is the moment of inertia with respect to the axis perpendicular to the plane of the triangle through the right angle vertex of the triangle.

### 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

### Rotational Equilibrium: Balancing a tray with hand and thumb

You are holding a lunch tray from one end hand holding the tray(four fingers and thumb). Tray has plate and some beverage. A) What are the forces exerted by your hand on this tray.

### Static equilibrum

A weight W is supported by attaching it to a vertical uniform metal pole by a thin cord passing over a pulley having negligible mass and friction. The cord is attached to the pole 40.0cm below the top and pulls horizontally on it. The pole is pivoted about a hinge at its base, is 1.75m tall, and weighs 55.0N . A thin wire conn

### Tension of cable and magnitude of force

A uniform drawbridge must be held at a 37 degree angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 45,000 N and is 14.0 m long. A cable is connected 3.5 m from the hinge where the bridge pivots (measured along the bridge) and pulls horizontally on the bridge to hold it in place. a) What is t

### The Rotation of an Object Around a Fixed Axis

A merry-go-round is stationary. A dog is running on the ground just outside its circumference, moving with a constant angular speed of 0.750 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the merry-go-round one third of a revolution in front of him. At the instant the dog see

### 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

### the minimum coefficient of static friction

In a "Rotor-ride" at a carnival, people pay money to be rotated in a vertical cylindrically walled "room." If the room radius is 4.2 m, and the rotation frequency is 0.6 revolutions per second when the floor drops out, what is the minimum coefficient of static friction so that the people will not slip down?

### Non uniform circular motion: Total acceleration

A race car starts from rest on a circular track. The car increases its speed at a constant rate (At) as it goes 2.75 times around the track. Find the angle that the total acceleration of the car makes with the radius connecting the center of the track and the car at the moment the car completes its trip of 2.75 times around the

### Unitary matrices and their determinants

1. show that for a 2x2 unitary matrix its determinant is a complex number of unit modulus 2. Verify that the Pi/2 rotation matrix is orthogonal. 3. Verify that the matrices: A= 1/sqrt(2) * ( 1 i ) ( i 1) and: B = 1/2 * ( 1+i 1-i ) ( 1-i 1+i ) are unitary. Verify

### Eigenvalues, eigenvectors, and other properties of given matrix

Consider the matrix A = (cos t sin t) (-sin t cos t) Show that it is unitary Show that the eigenvalues are exp(it) and exp(-it) find the eigenvectors Verify that U'AU is diagonal matrix, where U is the matrix of the eigenvectors. Show that since determinant of a matrix is unchanged under unitary change of

### 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

### Rotational simple harmonic motion: A hanging square frame

Square object of mass {m} is constructed of four identical uniform thin sticks, each of length {L}, attached together. This object is hung on a hook at its upper corner. If it is rotated slightly to the left and then released, at what frequency will it swing back and forth? Answer must be expressed in terms of the variables