Question

3. An evil professor invents a physics problem with no context and gives you the following dia- gram. Two rigid beams of an unimportant material, one of unknown length ri and the other of length r2 2.3 meters are affixed to each other and rotate around a black dot that usually repre- sents a pivot point in problems such as these. For no reason, a force Fi 3.1 N is exerted directly downwards at the end of the first beam. Likewise a force of unknown magnitude F2 is exerted at an unknown angle at the end of the second beam. The y-component of F2 is mercifully given by the professor as 4 N. 2m (a) What is the sign of the net torque exerted on the system of two beams? (b) What is the magnitude of the net torque exerted on the system of two beams? (c) If the angular acceleration of the two beams is 12.3 rad/s2, what is the moment of inertia of the two beam system?

Answer 1

Torque =Force *distance

Here Net Torque = $F_{1}*2m +F_{2y}*r_{2}$

since both forces cause rotation in counter clockwise direction sign positive(take counter clockwise rotation as positive)

a) ANSWER: + ve (counter clockwise)

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$\tau _{net}=F_{1}*2m +F_{2y}*r_{2}$

$\tau _{net}=3.1N*2m +4N*2.3m$

$\tau _{net}=3.1*2 +4*2.3$

b) ANSWER:$\tau _{net}=15.4Nm$

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(c) Torque =Moment of inertia * angular acceleration

$\tau =I\alpha$

$15.4Nm=I*12.3rad/s^{2}$

$15.4=I*12.3$

$I=15.4/12.3$

ANSWER: $I=1.252kgm^{2}$

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