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# Torques

### Determining how to exert the greatest torque on a tree.

A rope 20m in length is attached to a tree to pull it over. How far up the trunk of the tree should the rope be attached to exert the greatest torque?

### Calculating the holding torque in a gear box.

A gear box has the input power 10kw at 2400 rev/min. The gear ratio is a reduction of 2 to 1. The efficiency is 98%. What is the holding torque required?

### Modelling of a Controlled Cart on a Horizontal Pivoting Beam

Use Newtons Law to derive equations of motion for the system. This should be converted into transfer functions for input into MATLAB/SIMULINK. The system consists of a motorised trolley on a see-saw (see attached figure). The trolley motor is to be controlled and eventually the trolley must balance the beam. A potentiometer s

### Circular Steel Shaft with Varying Diameters and Torsional Loads

A circular steel shaft of the dimensions shown in the figure is subjected to three torques: T1=28 k-in, T2=-8 k-in, and T3 = 10 k-in. (a) What is the angle of twist of the right end due to the applied torques? (b) Plot the angle of twist diagram along the shaft. Let G=12 106 psi.

### Three-Phase Squirrel-Cage Induction Motor

A three-phase, 60 Hz, squirrel-cage induction motor draws a current of 385 amps per phase and a total active power of 2344 kW when operating at full load from a 4000 volt (line) supply. The corresponding speed is 709.2 rev/min. The stator is star-connected and the resistance between two stator live terminals is 0.1 ohms. The mac

### Mechanics Angular Acceleration Quantities

A uniform rigid disk of radius r and mass m rolls without slipping on a smooth horizontal surface. A constant force of magnitude P is applied to the rim of the disk at distance r above the horizontal surface and in the direction of motion. r,m,P are known. what is the angular acceleration in terms of known quantities, and wha

### Shunt-wound motor: Maximum start-up torque

(a) A shunt-wound motor set was designed to run from a 250 V d.c. supply. It had an effective armature resistance of 3 m Ohm and when run at 3000 rev/min it drew 10 kA. Find: (i) The maximum permissible supply voltage at start-up if the motor set is not to draw more than 20 kA when started from rest. (ii) The maximum start-

### Find the starting torque, the maximum torque, and the speed at maximum torque for a 3 phase, 50 Hz, 6 pole wound rotor induction machine.

A 3 phase, 50 Hz, 6 pole wound rotor induction machine has the following per phase parameters: Rs = Negligible Ls = 0.003 H Rr = 0.3 Ohm Lr = 0.002 H Lm = 0.1 H Rc = Infinity Ns/Nr = 1.2 The voltage applied to each phase is 240 Vrms. Find: the starting torque, the maximum torque, and the speed at max