Calculate the angular acceleration of the wheel, Mechanical Engineering

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.

1608_Calculate the angular acceleration of the wheel.png

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

2100_Calculate the angular acceleration of the wheel1.png

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.

Posted Date: 1/29/2013 2:12:55 AM | Location : United States







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