# Torque, angular acceleration, and moment of inertia

1. Jan 17, 2012

### chromium1387

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

t=Iα

3. The attempt at a solution
Okay, so we calculated the moment of inertia for each dumbbell by saying that each was 4R long. So, IA=m(2R)2+m(2R)2=8mR2 and IB=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

2. Jan 17, 2012

### ehild

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

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

ehild

3. Jan 18, 2012

### chromium1387

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