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Calculate the angular acceleration of the wheel:
A locomotive wheel of radius r = 0.8 m is illustrated in Figure. At the given instant, the speed of the locomotive is 1.6 m/sec and is accelerating at the rate of 2 m/sec2. Calculate the angular acceleration of the wheel and the acceleration of the points P1, P2, P3 and P4 lying on the vertical and horizontal diameters.
Solution
We have v A = r ω . P2 is instantaneous centre of rotation.
∴ ω = vA / r= 1.6/0.8 = 2 rad / sec
a A = r α
∴ α = a A / r = 2/0.8 = 2.5 rad / sec2
Supposing the wheel to be moving towards the right as illustrated ω and α will be in the clockwise direction.
Accelerations of P1, P2, etc. can be calculated very easily from the equations derived above.
aA t^ = a α = 2 m/sec2
a A n^ = a ω2 = 3.2 m / sec 2
Point P1
tan θ =2/1.2 = 1.67
θ = 59.03o
∴ a p2 n = 3.2 m/sec2
Likewise for point P2, acceleration of P3 and P4 can be calculated in the same way.
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