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Rotation

Moment of Inertia

Ball a, of mass m_a, is connected to ball b, of mass m_b, by a massless rod of length L. The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system abou

magnetic flux and Faraday's law

1.) Suppose the largest surface of the body through which flux passes has an area of 0.024 m2 and a normal that is parallel to a magnetic field of 2.0 T. Determine the smallest time period during which the field can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V. For this one

Find the condition for the borderline case

A fountain has jets that squirt water in all directions at a speed of 16 ft/sec from a central point as shown. The dotted curve shows the boundary between the "dry" region (which the fountain doesn't reach) and the "wet" region reached by the water spray. Find the shape of this dotted curve, giving an equation for it (y as a f

Finding the Moment of Inertia of a Uniform Thin Square

Starting from the sum (attached) and replacing it by the appropriate integral, find the moment of inertia of a uniform thin square of side 2b, rotation about an axis perpendicular to the square and passing thought its center.

Physics Problems.

6. If F1=50lb upward and F2=60lb upward ,the resultant and the direction of the resultant along the common line of action would be (A)10lb down (B)90lb up (C)110lb up (D)210lb up 7. A body that weighs 50lb is placed in contact with an inclined plane surface. The coefficient of friction between the surfaces is 0.25 and the angle

Rigid body rotation and moment of inertia

A rotating door is made from fr rectangular glass panes, as shown in the drawing. The mass of each pane is 79 kg. A person pushes on the outer edge of one pane with a force of F = 78 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration.

Angular motion: Rotational work and energy

(a) Calculate the kinetic energy that the earth has because of its rotation about its own axis. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 9.33 109 J. (b) Calculate the kinetic energy that the earth ha

Finding Force, Horizontal and Vertical Component

A woman who weighs 489 N is leaning against a smooth vertical wall, as the drawing shows. (a) Find the force FN (directed perpendicular to the wall) exerted on her shoulder by the wall. (b) Find the horizontal component of the force exerted on her shoes by the ground. (c) Find the vertical component of the force exerte

Rigid Objects in Equilibrium

In an isometric exercise a person places a hand on a scale and pushes vertically downward, keeping the forearm horizontal (please see attachment). This is possible because the triceps muscle applies an upward force M perpendicular to the arm, as the drawing indicates. The forearm weighs 25.0 N and has a center of gravity as indi

Rotational motion problems

At t=3s, a point on the rim of a .2m radius wheel has a tangential speed of 50m/s as the wheel slows down with a tangential acceleration of constant magnitude 10m/s^2. a) What is the constant angular acceleration? b) What is the angular velocities at t=3s & t=0s c) Through what angle did the wheel turn between t=0s & t=3s?

Strobe Light on a Fan

1. A strobe lights shines on a fan. By changing the speed of the strobe light, the fan appeared to run slower and sometimes even looked like it was stopping or running backwards. Assume the fan has three identical blades so that once the fan has rotated 1/3 around it looks exactly the same. Before turning on the strobe light we

Angular Velocity and Mass

Problem # 12 - A thin ring having a mass of 15 kg strikes the 20-mm-high step. Determine the largest angular velocity w1 the ring can have so that it will not rebound off the step at A when it strikes it. See attached file for full problem description and diagram.

A hoop of mass M and radius 1? rolls without slipping along a track which has the shape of a circle with radius 4R. It is subject to gravity. It is confined to a plane, so when the no-slip constraint is imposed there is just one degree of freedom. Find T, U, L, and the Lagrange equation. For small oscillations find the angular frequency of oscillation.

A hoop of mass M and radius 1? rolls without slipping along a track which has the shape of a circle with radius 4R. It is subject to gravity. It is confined to a plane, so when the no-slip constraint is imposed there is just one degree of freedom. Use the angle d as your coordinate. (This angle gives the location of the cente

Magnetic Field Intensity

1. A disc of Radius a lies on x-y plane with the z axis through its center. Surface Charge of uniform density P (row ) lies on the disk, which rotates about the Z axis at an angular velocity (ohm sign) rad/s. Find H (magnetic field intensity) at any point on the Z axis. Use BIOT-SAVART LAW. 2. A solid cylinder of radiu

Calculating the moment of inertia

An object is made up of three masses connected by massless rods of fixed length. Mass A is located at (30.0 cm, 0 cm) and has a mass of 250 grams, mass B is located at (0 cm, 40.0 cm) and has a mass of 350 grams, mass C is located at (-20.0 cm, 0 cm) and has a mass of 450 grams. What is the moment of inertia of this object about

Electricity & Magnetism Qualitative Problems

Here is a list of Qualitative problems which need the physics explained for each, diagrams, and equations with text are welcome. 1) The vector potential and the magnetic field inside and outside of a diamagnetic sphere in a uniform magnetic field 2) The vector potential and the magnetic field inside and outside of a unif

Basic Conceptual Physics

1. A ball is thrown up in the air. It goes up and then eventually comes down again. On its way up (after being let go), which is correct? A. Its acceleration decreases B. Its acceleration increases C. Its accelerations stays pretty much the same D. Impossible to stay unless the ball,s mass is known E. Impossible to sta

Angular acceleration of the disk

In problem 16.98(a), if the disk and drum have a total weight of 15 lb, and P has a magnitude of 4 lb, the angular acceleration of the disk is: a. 16.4 rad/s^2 b. 12.4 rad/s^2 c. 23.2 rad/s^2 d. 8.3 rad/s^2

Calculate the moment of inertia of a homogeneous cube

Calculate the inertia tensor of a homogeneous cube of mass M and density D and sides b. Let one corner be at the origin and the 3 sides lie along the coordinate axes. Please show all work including the matrix expansion in detail...I need to see how the tensor equation is used to generate a moment of inertia.

Stroboscope & frequency of flashing light

Please help with the following problem. A stroboscope is a light that flashes on and off at a constant rate. It can be used to illuminate a rotating object, and if the flashing rate is adjusted properly, the object can be made to appear stationary. (a.) What is the shortest time between flashes of light that will make a thr

Fractional excitation of a two-state ensemble

Temperature plays a role in determining the relevance of electronic, vibrational, and rotational spectral lines in room-temperature biomedical optics. The ratio between any two states' populations is an exponential function of ∆E, the difference in their energies, and kT, the Boltzmann energy, ratio is exp (-∆E=kT). Taki

Angular speed and rotational inertia of the cylinder

Show ALL your work, including the equations used to solve the problems. A uniform cylinder of radius 10 cm and mass 20 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0 cm form the central longitudinal axis of the cylinder. a) What is the rotational inertia of the cylinder about the axis

Plane Mirror and Light Rays

I had some questions about mirrors, please provide supporting equations and information for these problems. - Does the mirror equation (p^-1 + d^-1 = 2R^-1 = f^1) apply to a plane mirror? What relationship between p and d does it imply? - Why is it when you stand in front of a mirror your left appears on your right and your

The Magnitude and Direction of Centripetal Acceleration

What is the magnitude and direction of the centripetal acceleration due to the earth's rotation at a location near Kansas City at 38 degrees latitude? I believe the answer is 2.66x10^-2 m/s^2, towards the earth's rotation axis. I need to see all formulas involved.

Multiple Choice Question son Velocity and Tension

A particle moves according to the equation x = 10t2, where x is in meters and t is in seconds. Find the average velocity for the time interval from 2.0 second to 3.0 second. 50 m/s 100 m/s 250 m/s 200 m/s A particle undergoes three consecutive displacements: d1 = (10i + 30j + 12k), d2 = (23

Frequency and amplitude of emf in wire loop

A stiff wire bent into a semicircle of radius a=2.0 cm is rotated at constant angular speed 40 rev/s in a uniform 20 mT magnetic field. What are the (a) frequency and (b) amplitude of the emf induced in the loop?

Moment of inertia - Parallel-Axis Theorem

To solve many problems about rotational motion, it is important to know the moment of inertia of each object involved. Calculating the moments of inertia of various objects, even highly symmetrical ones, may be a lengthy and tedious process. While it is important to be able to calculate moments of inertia from the definition, in