4. A block of mass 3.0kg hangs from one end of a cord, while the other end is wr

Question

4. A block of mass 3.0kg hangs from one end of a cord, while the other end is wrapped around a uniform wheel of radius 30cm and moment of inertia 0.80kgm2. The wheel is free to rotate about a frictionless horizontal axis through the center. The system starts from rest and the cord unravels with no slippage. (A) Find the linear acceleration of the block. (B) Find the angular velocity of the wheel after the block has dropped through a distance of 1.50m.

Explanation / Answer

Torque to the wheel T=MgR=3*9.8*0.3=8.82 Nm T=I*a/R (where I is moment of inertia) A)a=T*R/I =8.82*0.3/0.8 =3.3075 m/s2 B)s=0.5a(t^2) (where s is the distancce travelled) =>t^2=1.5*2/3.3075 =>t=0.95 sec v=at =3.3075*0.95 =3.15m/s angular velocity=v/R =10.5 radian/sec

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