A wheel of a car has moment inertia of 1.7kg.m^2. when tested for dynamic balanc
ID: 1780672 • Letter: A
Question
A wheel of a car has moment inertia of 1.7kg.m^2. when tested for dynamic balance it is accelerated from rest to a speed of 1600RPM by a difference of applied effort (22.9 N.m) and the resistance torque (2.1 N.m) calculate time taken for wheel to reach final speed and the number of turns made by the wheel to reach final speed. A wheel of a car has moment inertia of 1.7kg.m^2. when tested for dynamic balance it is accelerated from rest to a speed of 1600RPM by a difference of applied effort (22.9 N.m) and the resistance torque (2.1 N.m) calculate time taken for wheel to reach final speed and the number of turns made by the wheel to reach final speed. A wheel of a car has moment inertia of 1.7kg.m^2. when tested for dynamic balance it is accelerated from rest to a speed of 1600RPM by a difference of applied effort (22.9 N.m) and the resistance torque (2.1 N.m) calculate time taken for wheel to reach final speed and the number of turns made by the wheel to reach final speed.Explanation / Answer
Here, applied toque is given as 22.9Nm and resistance toque as 2.1Nm. So net toque moving the wheel is 22.9-2.1= 20.8Nm. Now, initial speed is given as Wi= 0 and final speed as 1600rpm , which, when converted to angular speed Wf= 2*3.14*1600/60= 167.47rad/s. So, applying formula, toque applied= Moment of inertia * angular acceleration which gives angular acceleration= 20.8/1.7= 12.23rad/s^2
Now, time taken to reach final speed= final speed - initial speed / acceleration= 167.47-0/12.23= 13.7s
Also, Wf^2- Wi^2= 2*angular acceleration*theta
Or, theta= 167.47^2 / 2*12.23= 1146.6 rad. Now, as number of turns is to be found, theta/2*pi= 1146.6/6.28= 182.58 turns.
So, the number of turns made by the wheel to reach final speed= 182.58.
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