Mechanical Engineering Principles

112 MECHANICAL ENGINEERING PRINCIPLES Now try the following exercise Exercise 45 Further problems on work done and power transmi ...

TORQUE 113 In general, this may be written as: Total kinetic energy= (∑ mr^2 )ω^2 2 =I ω^2 2 whereI(=mr^2 )is called themoment ...

114 MECHANICAL ENGINEERING PRINCIPLES Problem 13. A system consists of three small masses rotating at the same speed about the s ...

TORQUE 115 (b) Initial kinetic energy is given by: I ω^21 2 = ( 25 ) ( 450 × 2 π 60 ) 2 2 = 27 .76 kJ The final kinetic energy i ...

116 MECHANICAL ENGINEERING PRINCIPLES torque of 43.6 N m. Find the speed of the shaft (a) after 15 s, and (b) after the first fo ...

TORQUE 117 efficiency of the motor, (b) the speed of the driven pulley wheel. (a) From above, power output from motor =(F 2 −F 1 ...

118 MECHANICAL ENGINEERING PRINCIPLES Output power from motor =resistive force× velocity of train (from Chapter 14) = 20000 × 20 ...

TORQUE 119 The unit of power is: (a) N (b) J (c) W (d) N/m The unit of the moment of inertia is: (a) kg m^2 (b) kg (c) kg/m^ ...

10 Twisting of shafts At the end of this chapter you should be able to: appreciate practical applications where torsion of shaf ...

TWISTING OF SHAFTS 121 Rigid 2 R A B T L q g Figure 10.1 However, from equation (1.1, page 12),γ= τ G Hence, (τ G ) L=Rθ or τ R ...

122 MECHANICAL ENGINEERING PRINCIPLES However, from Table 7.1, page 91, the polar second moment of area of a circle, J= πR^4 2 , ...

TWISTING OF SHAFTS 123 and θ= 0 .0543 rad = 0 .0543 rad× 360 ° 2 πrad i.e. angle of twist,θ= 3. 11 ° Problem 2. If the shaft in ...

124 MECHANICAL ENGINEERING PRINCIPLES Figure 10.5, wherea>b. Determine the maximum resulting torque acting on the shaft and t ...

TWISTING OF SHAFTS 125 of twist of this shaft, due to this torque, over a length of 1 m, given that the rigid- ity modulus,G=40 ...

126 MECHANICAL ENGINEERING PRINCIPLES Assignment 3 This assignment covers the material contained in Chapters 8 to 10. The marks ...

Part 2 Dynamics 11 Linear and angular motion At the end of this chapter you should be able to: appreciate that 2πradians corres ...

128 MECHANICAL ENGINEERING PRINCIPLES Angular velocity The speed of revolution of a wheel or a shaft is usually measured in revo ...

LINEAR AND ANGULAR MOTION 129 Since a wheel is rotating at 573 revolutions per minute, then in 80/60 minutes it makes 573 × 80 6 ...

130 MECHANICAL ENGINEERING PRINCIPLES and time,t=10 s. Hence,angular acceleration, α= 800 × 2 π 60 − 300 × 2 π 60 10 rad/s^2 = 5 ...

LINEAR AND ANGULAR MOTION 131 Table 11.1 s =arc length (m) r =radius of circle (m) t =time (s) θ =angle (rad) v =linear velocity ...