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# A string is wrapped on a wheel of moment of inertia 0.20 kg-m^{2} and radius 10 cm and goes through a light pulley to support a block of mass 2.0 kg as shown in figure (10-E5). Find the acceleration of the block.

Answer :

The acceleration of the block is given as

Given

The moment of the inertia of the wheel is given as 0.20 and a radius of 10 cm to support/hang a block of 2 kg mass.

Formula Used

The formula used to find the torque applied on the pulley due to the masses are described below as the product of moment of Inertia and angular acceleration:

where

is the torque of the pulley, is the angular acceleration and I is the moment of Inertia of the pulley

Explanation

The tension applied by the block on the string is given as

The torque of the pulley is given as

Hence, making the moment of Inertia of the pulley as

Now calculating the acceleration in terms of angular acceleration is

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Figure 5.9 shows (v_{x} ,t ),and( (v_{y} ,t) diagrams for a body of unit mass. Find the force as a function of time.

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