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.

Explanation

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`