A wheel of mass 1.4 kg and radius 0.4 m is mounted on a frictionless, horizontal axle as shown in Fig. 7.2.50. Alight string wrapped around the rim supports a mass of 2 kg. What is the angular acceleration of the wheel and the tangential acceleration of a point on the rim ? Also find the tension in the string.

A wheel of mass 1.4 kg and radius 0.4 m is mounted on a frictionless,

1.	A wheel of mass 1.4 kg and radius 0.4 m is mounted on a frictionless, horizontal axle as shown in Fig. 7.2.50. Alight string wrapped around the rim supports a mass of 2 kg. What is the angular acceleration of the wheel and the tangential acceleration of a point on the rim ? Also find the tension in the string.
Answer» Solution :Mass of wheel = m = 1.4 kg Radius = r=0.4 m ANGULAR acceleration of the wheel `=ALPHA`= ? `tau = I alpha = Tr` `1/2 mr alpha = T` tangential acceleration `a = ralpha` `T = 1/2 ma` When the mass falls downwards with an acceleration a, `m_(1)g -T = m_(1)a` `m_(1)g -1/2 ma = m_(1)a` `a(m_(1) + m/2) = m_(1)g, a =(m_(1)g)/(m_(1) + m/2) = (2 xx 9.8)/(2 + (1.4)/2)` Tangential accelerations `=a= 7.26 m//s^(2)` Angular acceleration `=alpha = a/r = (7.26)/0.4 = 18.15 m//s^(2)` Tension in the STRING `=T= 1/2 ma = 1/2 xx 1.4 xx 7.26 = 5.1 N`