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

A, B, D

Explanation

In this problem the rod has a mass 1 kg
a. `tau_(net)=tau_(net)xxalpha` ltbr. `rarr 15=(1.75+0.084)alpha`
`rarr alpha=1500/(175+8.4)=1500/183.4`
`=8.1rad/s^2 (g=10)`
`=8.01rad/s^2 (if g=9.8)`

`b. T_1-m_1g=m_1a`
`rarr T_1=m_a+m_1g`
`=2(a+g)=2(alphar+g)`
`=2(8xx0.5+9.8)`
`=2xx13.8`
`=27.6N` onthe first body
in the second body
`rarr m-2g-T_2=m_2a`
`rarr T_2=m_2g-m_2a=5(g-a)`
`=5(9.8-8xx0.5)`
`=5xx5.8=29N`