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» <html><body><p></p>Solution :Mass of wheel = m = 1.4 kg <br/> Radius = r=0.4 m <br/> <a href="https://interviewquestions.tuteehub.com/tag/angular-11524" style="font-weight:bold;" target="_blank" title="Click to know more about ANGULAR">ANGULAR</a> acceleration of the wheel `=<a href="https://interviewquestions.tuteehub.com/tag/alpha-858274" style="font-weight:bold;" target="_blank" title="Click to know more about ALPHA">ALPHA</a>`= ? <br/> `tau = I alpha = Tr`<br/> `1/2 mr alpha = T` <br/> tangential acceleration `a = ralpha` <br/> `T = 1/2 ma` <br/> When the mass falls downwards with an acceleration a, <br/> `m_(1)g -T = m_(1)a` <br/> `m_(1)g -1/2 ma = m_(1)a` <br/> `a(m_(1) + m/2) = m_(1)g, a =(m_(1)g)/(m_(1) + m/2) = (2 xx 9.8)/(2 + (1.4)/2)` <br/> Tangential accelerations `=a= 7.26 m//s^(2)` <br/> Angular acceleration `=alpha = a/r = (7.26)/0.4 = 18.15 m//s^(2)` <br/> Tension in the <a href="https://interviewquestions.tuteehub.com/tag/string-11290" style="font-weight:bold;" target="_blank" title="Click to know more about STRING">STRING</a> `=T= 1/2 ma = 1/2 xx 1.4 xx 7.26 = 5.1 N`</body></html>