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Rotation

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

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

relative speed and angular velocity

Please see the attached file. Please include all vector diagrams. Point A of the link BA has a downward velocity of Va = 2 m/s during an interval of it's motion. For the position where ø = 30 degrees determine the angular velocity of AB and determine the velocity (Vg) of the midpoint G of the link.. Solve the relati

angular velocity of link BC

Please see attachment. Determine the angular velocity of link BC for the instant indicated given 2 cases: Case a: the center of the disk is fixed pivot and the disk rotates about this pivot with angular velocity Ω. Case b: the disk rolls without slipping on the horizontal surface with angular velocity Ω.

Relative Motion, Velocity, and Rotation

Please see attached file for more information. The unit at A consists of a consists of a high torque geared motor which rotates link AB, in the counterclockwise direction at (theta dot) = .5 rads per second. Unit A is free to roll along the horizontal surface and point C is anchored. Determine the velocity of unit A when

Rotation of Rigid Bodies

Please see the attached file. Two V belt pullies form an integral unit and rotate about a fixed axis at O. At a certain instant point A on the belt of the smaller pully has a velocity of Va = 1.5 m/s. and point B on the belt of the larger pully has an acceleration of ab = 45m/s as shown. For this instant determine the ac

Torque

A force F of magnitude F making an angle theta with the x axis is applied to a particle located along axis of rotation A, at Cartesian coordinates (0, 0) The vector F lies in the xy plane, and the four axes of rotation A, B, C, and D all lie perpendicular to the xy plane. a). What is the torque (TA) about axis A due to the fo

Rigid Body Kinematics

The circular disk rotates with a constant angular velocity w=40 rads/sec about its axis which is inclined in the Y-Z plane at the angle A = arctan ¾. Determine the vector expressions for the velocity and acceleration for point P located on the rim, whose position vector at the instant shown is r = 15i + 16j -12k in. (Plea

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

The North Pole

Explain why one cannot find the North Pole of the Earth using only a simple compass.

Vector calculus

Given vector function V = xyi + 2yzj +3zxk, a) what is the curl of this function, and b) is there more net rotation at the origin or at (1,1,1)

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

Angular Acceleration and Angular Velocity

Please help me with the the steps. 1. A 0.12 m radius grinding wheel takes 5.5 sec to speed up from 2.0 rad/sec to 11.0 rad/sec. What is the wheel's average angular acceleration? 2. A solid sphere of mass 4.0 kg and radius 0.12 m is at rest at the top of a ramp inclined 15 degrees. It rolls to the bottom without slipping. Th

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.

Effort required for lifting a rock using a crowbar lever

Using a 1-meter crowbar to lift a 50-kg rock. The crowbar is placed over a small rock set .25 meters from the end of the crowbar, which is placed under the rock. The crowbar is set at a 30-degree angle from the ground. I need to figure out how much effort must be applied to the crowbar to lift the rock and what kind of lever th

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