# How is tension in a string affected by moment of inertia?

## Homework Statement

I'm in need of a more conceptual answer, rather than numerical.

Say you have a block on a horizontal frictionless table (block 1). Then you have a string tied to block one and strung over a pulley that is at the right end of the table (the pulley has mass). On the other end of the pulley, there is another block hanging there connected by the same string (block 2). So the tension in the string will be different for block 1 and block 2.

I'm trying to figure out a way to find the acceleration of the system. I know that gravity will act on block 2 and cause it to accelerate downwards. So block 2 will cause a clockwise torque on the pulley. I'm confused about block 1. How would you find the tension in the string for block 1? Since there's no friction, shouldn't block 1 not resist the force that block 2 is providing?

I found a source online that says the tension in the string for block 1 (causes counter clockwise torque) will act against the acceleration of block 2 (causes clockwise torque). But here's my question: If the tension in the string for block 1 is resisting the acceleration of block 2, then why does block 1 still move TO THE RIGHT, when the only force acting on it is the tension in the string, which supposedly acts TO THE LEFT against the acceleration of block 2.

## Homework Equations

(T2 * R) - (T1 * R) = 1/2MRR * (a/R)
• So in this equation you can see that tension for block one acts against the tension for block 2.

mg - T2 = m2 * a
• One of the equations to find the acceleration of system

T1 = m1a
• So here it says that the tension in the string for block 1 equals the force applied to block 1. So why does block 1 move to the right when it's tension is supposedly acting to the left?
• T1 acts to the left (counter clockwise torque) and T2 acts to the right (clockwise torque).... so why does block one move to the right, when the only force acting on block one is T1 (which acts to the left)?

## The Attempt at a Solution

Again, not numerical, just conceptual explanation would be great. Thanks in advance!

haruspex
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shouldn't block 1 not resist the force that block 2 is providing?
It has inertia, which means it resists acceleration.
why does block 1 still move TO THE RIGHT, when the only force acting on it is the tension in the string, which supposedly acts TO THE LEFT
Tension (likewise compression) is better thought of as pairs of opposing forces. Pick a small element of the string. The tension provides a force to the right on the right hand of the element and a force to the left on the left.