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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

### 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

### 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

### 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

### 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

### 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

### Circuit analysis and efficiency

A fully loaded 440V, three phase motor draws 12.4A at 86% power factor (pf). Its speed is 1730 rpm and its torque output to a mechanical load is 29.1 lb-ft*1.356=39.5Nm. What is the output HP and the efficiency?

### Power Screws

A power square thread screw has a pitch diameter (dm) of 34mm, the lead of the screw 1 of 4mm, the frictional diameter of the collar (dc) of 40mm. The coefficients of friction are f=0.08 for the threads and fc=0.05 for the collar. the vertical load F per screw is 5 kN. How do I find the torque required to raise the load?

### Solve: Computing the Torque

A force of 30N is applied perpendicularly to the face of a door at a distance of 1.5 m from the hinge of the door. Find the torque on the door about its hinge: a. 20 n/m b. 2nm c. 45Nm d. 20Nm

### Pressure problem

A hydraulic press for compacting powdered samples has a large cylinder which is x = 11.8 cm in diameter, and a small cylinder with a diameter of y = 1.96 cm (see figure). A lever is attached to the small cylinder as shown. The sample which is placed on the large cylinder, has an area of 4.09 cm2. What is the pressure on th

### A pressure problem using different areas

A hydraulic press for compacting powdered samples has a large cylinder which is x = 11.8 cm in diameter, and a small cylinder with a diameter of y = 1.96 cm (see figure). A lever is attached to the small cylinder as shown. The sample which is placed on the large cylinder, has an area of 4.09 cm2. What is the pressure on the

### Stress Conditions, Etc.

A simple explanation of these solutions would be much appreciated. Could you also include any relevant comment along the way to help me understand your method and this subject better? Sketches are required. Can you also include Mohr's circle? Please find the questions in the attachment below. Hope you can help with this revis

### Torque, Inertia, Acceleration, Velocity, and Kinetic Energy

A belt drives a pulley of radius 4.0 cm and negligible mass as shown. The pulley is attached to a larger, solid wheel of mass 60 kg and radius 30 cm that is initially at rest. The tension T1 in the belt is 150.0 N and the tension T2 is 50 N. What is the total, net torque on the pulley? What is the moment of inertia of the whe

### Rotational Dynamics and Tangential Acceleration

A meterstick pivoted about a horizontal axis through the 0 cm end is held in a horizontal position and let go. (a) What is the tangential acceleration of the 100 cm position? (b) Which position has a tangential acceleration equal to the acceleration due to gravity?