Question

At one instant a bucket ( mass 2kg) is supported from a non-ideal pulley ( radius = .1 meters, mass 2kg). the pulley is free to turn. compute the angular acceration of the pulley and the linear accerleration of the bucket.

Answer 1

Here pulley radius = 0.1 m

mass of pulley = 2 kg

So moment of intertia of pulley = MR² / 2 [because it is disc]

SO M.I = (2 * 0.1* 0.1) / 2 = 0.01

As we know tha torque = M.I * angular acceleration

So ANgular Acc= Torque / M.I.

Also Here Torque = Ext. Force * radius [ External force is due to bucket = mg = 2 * 9.8 = 19.6 N]

SoTorque= 19.6 * 0.1 = 1.96

So Angular Acc= 1.96/ 0.01 = 196 rad/s²

===> And    Linear acceleration is equal to acc due to gravity because object is free to move and moving due to g. So Linear Acc=9.8 m/s²