Torque, angular acceleration, and moment of inertia

[chromium1387]

Homework Statement

We did this question today in class, but looking back at it, I'm kind of confused.

Two identical dumbbells are formed by placing equal point masses at either end of two identical light (ie. massless) rods. The rods are pivoted so that dumbbell A rotates around the centre of the rod, while dumbbell B rotates around a point a quarter of the way along the rod. If the same torque is applied to both rods, how will the resulting angular accelerations compare?

Homework Equations

t=Iα

The Attempt at a Solution

Okay, so we calculated the moment of inertia for each dumbbell by saying that each was 4R long. So, I_A=m(2R)²+m(2R)²=8mR² and I_B=m(R)²+m(3R)²=10mR². Because B has a larger moment of inertia, does it not need a greater angular acceleration than A if the same torque is applied? :S

 

[ehild]

t=Iα

I_A=8mR² and I_B=10mR². Because B has a larger moment of inertia, does it not need a greater angular acceleration than A if the same torque is applied? :S

Look at the first equation: t(torque)=I(moment of inertia) * α(angular acceleration)
t is the same for both dumbbells : I_Aα_A=I_Bα_B

Substitute for the I-s. Which angular acceleration is greater?

ehild

 

[chromium1387]

oh, wow. i was definitely thinking backwards for some reason. thank you for replying to my very silly question!