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Question Number 23932 by Tinkutara last updated on 10/Nov/17

A cord is wound around the circumference

of a bicycle wheel (without tyre) of

diameter 1 m . A mass of 2 kg is tied at

the end of the cord and it is allowed to

fall from rest . The weight falls 2 m in 4

s . The axle of the wheel is horizontal

and the wheel rotates with its plane

vertical . If g = 10 {ms}^{- 2}, what is the

angular acceleration of the wheel ?

Answered by ajfour last updated on 10/Nov/17

s = \frac{1}{2} (α R) t^{2}

\Rightarrow α = \frac{2 s}{t^{2} R} = \frac{2 \times 2}{16 \times (1 / 2)} = 0.5 r a d / s^{2} .

Commented by Tinkutara last updated on 10/Nov/17

Why acceleration of mass is linear

acceleration of wheel ?

Commented by ajfour last updated on 10/Nov/17

b e c a u s e a s m u c h t h e c o r d u n w i n d s

s o m u c h t h e m a s s c o m e s d o w n .

R d θ = d y

\Rightarrow R (\frac{d θ}{d t}) = \frac{d y}{d t}

\Rightarrow R (\frac{d^{2} θ}{{d t}^{2}}) = \frac{d^{2} y}{{d t}^{2}}

a_{w h e e l} = α R = a_{m a s s} .

Commented by Tinkutara last updated on 10/Nov/17

Thank you very much Sir!