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# Torques

### Application of the Principle of Conservation of Angular Momentum

A student on a piano stool rotates freely with an angular speed of 3.16 rev/s. The student holds a 1.50 kg mass in each outstretched arm, 0.794 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.45 kg*m2, a value that remains constant. As the student pulls his

### Rotational Axes and Maximum Stresses

See the attached file. 1. Two solid aluminum shafts (G = 3.7x106 psi) are connected by the gears shown. Ends B and D are fixed. What is the angle through which end C rotates? 2. For the beam of the cross section shown, determine the location of the neutral axis from the bottom of the beam. 3. For the beam of question

### Three problems on torque

1. At the local playground, a 16 kg child sits on the end of a horizontal teeter-totter, 1.5m from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of 95 N. In which direction does the teeter-totter rotate if the adult applies the force of a distance (a) 3.0 m, (b) 2

### Physical Pendulum: Derive the equation for the period

A physical pendulum is constructed from a uniform thin rod of length L suspended from one end. The center of gravity lies at the midpoint of it's length. 1) Derive the equation for the period of this physical pendulum, assuming only small angle oscilllations. 2) Derive the equation for the angular frequency of this physic

### Moment of a Force: Normal Force on the Wheels

A jet transport has a weight of 1.00x10^6 N and is at rest on the runway. The two rear wheels are 15m behind the front wheel, and the plane's center of gravity is 12.6m behind the front wheel. Determine the normal force exerted by the ground on the front wheel and each of the two rear wheels.

### Rotational Dynamics

Please help with the following problem. By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly one-half the acceleration due to gravity. N

### Theory of ballpoint pen.

Describe the energy changes that take place when a ballpoint pen is used. Decribe the forces that act in the use the ballpoint pen..

### Mass Moment of Inertia of the Pulley

At the instant shown in the figure, the stepped pulley rotates clockwise at 25 rad/sec, with a clockwise angular acceleration of 6 rad/sec^2. The masses of the two blocks are mA = 0Kg, ma = 5Kg, and the cables are inextensible. Find the mass moment of inertia of the pulley. (See attached file for full problem description)

### Find the Tension in the Right Cable

See the diagram in the attached file. A window washer with a mass of 63.0 kg stands a distance, D = 0.800 m, from the left end of a plank of length, L= 1.90 m, with a mass of 17.0 kg. The plank is hung on two cables as shown. Find T2, the tension in the right cable.

### Two People Carrying a Mass Along an Inclined

Assume that W = 1.80 m, L = 3.30 m, angle = 21.0°, and that the weight of the mass is 39.90kg. What is the (vertical) weight carried by the builder at the rear? How do I set up the problem??

### A Beam on Wall

A 30.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of q = 24.5o with respect to horizontal, what is the horizontal component of the force exerted by the hinge on the beam? (Use the `to the right' as + for

### Rotational Motion: Wheel is pulled on a curb.

(See attached file for full problem description with diagram and values) --- You are trying to raise a bicycle wheel of mass and radius up over a curb of height . To do this, you apply a horizontal force . 1. What is the least magnitude of the force that will succeed in raising the wheel onto the curb when the

### Zero Net Torque Conditions

Please see attachment for torque diagrams. Each of the four bars shown can rotate freely in the horizontal plane about its left end. For which diagrams is the net torque equal to zero?

### A rope is wrapped around a wooden cylinder that turns on a metal axle. A crate is suspended from the free end of the rope. One end of the axle pivots on frictionless bearings; a crank handle is attached to the other end. When the crank is turned, the end of the handle rotates about the axle in a vertical circle, the cylinder turns, and the crate is raised. To determine magnitude of the force applied tangentially to the rotating crank.

The mechanism shown in the figure (see attachment) is used to raise a crate of supplies from a ship's hold. The crate has total mass 56 kg . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.310 m and a moment of inertia = 2.40 kgm^2 about the axle. The crate is suspended from

### Forces and are applied tangentially to a wheel with radius 0.330 m,

Forces and are applied tangentially to a wheel with radius 0.330 m, as shown in the figure . See attachment for diagram and figures. What is the net torque on the wheel due to these two forces for an axis perpendicular to the wheel and passing through its center?

### Angular Speed of System

A uniform rod of mass m_1 and length L rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass m_2, are mounted so that they can slide along the rod. They are initially held by catches at positions a distance r on each side from the center of the rod, and

### Torque and moments of force

Calculate F1 for the beam shown in figure below. Assume it is uniform and has a mass of 240 kg. For the distances assume that D1 = 1.86 m, D2 = 3.96 m, D3 = 2.82 m and D4 = 1.02 m. For the forces assume that f3 = 3940 N, f4 = 3140 N and f5 = 2100 N.

### Friction: Condition for Slipping or Toppling

A cube of side L = 1.40 m rests on a rough floor. It is subjected to a steady horizontal pull, F, exerted a distance h = 0.82 m above the floor as shown in figure below. As F is increased, the block will either begin to slide, or begin to tip over. What must be the coefficient of static friction μs so that the block begins to s

### Torque and potential energy in a current carrying coil

4) A circular coil with area A and N turn is free to rotate about a diameter that coincides with the x-axis. Current I is circulating in the coil. There is a uniform magnetic field B in the positive y-direction. Calculate the magnitude and direction of torque and the value of the potential energy U, as given in the equation; "U

### For and troque acting on a current carrying coil

3. A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current 1.40 A, is oriented with the plane of its loop perpendicular to a uniform 1.50 T magnetic field as shown below. a) Calculate the net force and torque which the magnetic field exerts on the coil. b) The coil is rotated through a 30.0º angle about the axis

### Shear Stress Problem for Pitch Circle Diameter

Shear stress problem -------------------------------------------------------------------------------- My answer to question 5 is wrong, can you correct? PCD = pitch circle diameter Factor of safety = ultimate tensile stress / safe working stress

### Torque and angular acceleration

Find the mass of a uniform solid cylinder which is mounted so that it can rotate freely (i.e., without friction) about a fixed axis that passes through its center and runs along the length of the cylinder. This is not a simple project because for one thing, that cylinder is heavy! Also you don't want to risk removing the heavy c

### Angular Acceleration of a Roller

A roller is rolled by pulling on a rope wrapped around an inner groove, as shown in attachment. If the roller rolls without slipping, the angular acceleration in rad/sec^2 of the roller is what? (See attached file for full problem description)

### Circular Frequency of a Rod

A slender rod is pivoted at 0 which is a frictionless bearing. The circular frequency in rad/s at the rod for a small oscillation is? (See attached file for full problem description)

### Physics Problem - A uniform, hollow, cylindrical spool

Please help with the following classical mechanics problem. See attached file for full problem description. --- A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R and mass M as in the attached .jpg. It is mounted so that it rotates on a fixed horizontal axle. A counterweight of mass m is connecte

### Motor Torques

Q1) Assume the torque stays constant at 120 N-m. How long will it take for the unloaded armature to accelerate from zero up to full speed of 3000 rpm? Now I am given the formular Ix = I w-wo / t. All I know is that the rotational inertia is 2.81 kg-m^2. Q2) What will be the power of the motor when it is s

### Circular Motion of a Particle

A particle of motion is moving in such a way that its position at time t is given by (t^3-3t, 4t^2, 5t).... See the attached file.

### Dipole Moments

Please show all work and show all equations used so I can understand completely. 1) A uniform electric field of 300N/C makes an angle of 25 degrees with the dipole moment of an electric dipole. If the torque exerted by the field has a magnitude of 2.5*10^-7N.m, the dipole moment must be ___? 2) The dipole moment of a dip

### Solving a Rigid Body Problem Using Newton's Second Law of Motion

See the attached file. A car has a mass of 1.4 tonnes. The distance between the front and rear wheel axles is 3.6m and the centre of mass is positioned 1.5m behind the front wheel centre and 0.8m above the road level. These details are attached in Figure Q1. The car, initially traveling at 12.6km/h, is accelerated up a stra