7.5 Normal and Tangential Coordinates (n − t)
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Figure 7.29: Infinitesimal change in the velocity and the relationship with the acceleration represented in n-t coordinate system ([3], pp. 55) as the magnitude and the direction must not be changed. For the problem using the x-y and the n-t coordinate frames, the following may be stated: v = vx i + vy j = vet a = ax i + ay j = an en + at et Example 7.14 ([3], Prob. 2/122) The camshaft drive system of a four-cylinder automobile engine is shown. As the engine is revved up, the belt speed v changes uniformly from 3 m/s to 6 m/s over a 2 second interval. Calculate the magnitudes of the accelerations of point P1 and P2 half way through this time interval. Solution: Since the timing belt velocity is increased uniformly, the (tangential) acceleration is constant. Therefore at =
dv ∆v 6−3 = = = 1.5 m/s2 dt ∆t 2
This constant acceleration also implies that, at the time half of the interval, the belt speed is 3+6 = 4.5 m/s v= 2 Point P 1 is moving in circular path around the sprocket. Therefore it will have both the tangential and normal components of the acceleration. The Chulalongkorn University
Phongsaen PITAKWATCHARA