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/sec^{2}. Calculate the angular acceleration of the wheel and the acceleration of the points P_{1}, P_{2}, P_{3} and P_{4} lying on the vertical and horizontal diameters.
Solution
We have v A = r ω . P_{2} is instantaneous centre of rotation.
∴ ω = v_{A} / r= 1.6/0.8 = 2 rad / sec
a _{A } = r α
∴ α = a A / r = 2/0.8 = 2.5 rad / sec^{2}
Supposing the wheel to be moving towards the right as illustrated ω and α will be in the clockwise direction.
Accelerations of P_{1}, P_{2}, etc. can be calculated very easily from the equations derived above.
a_{A }t^ = a α = 2 m/sec^{2}
a _{A }n^ = a ω^{2} = 3.2 m / sec ^{2}
Point P1
tan θ =2/1.2 = 1.67
θ = 59.03^{o}
∴ a _{p2} n = 3.2 m/sec^{2}
Likewise for point P_{2}, acceleration of P_{3} and P_{4} can be calculated in the same way.