1. What is the rotational analog to Newton\'s second law (F=ma)? 2. A point mass

Question

1. What is the rotational analog to Newton's second law (F=ma)? 2. A point mass is rotating about a rotation axis. You increase its distance from that axis by a factor of two. By what factor does its moment of inertia about the axis increase? 3. A solid disk is rotating about an axis with uniform angular velocity. Another disk (with the same moment of inertia about the rotating axis)is dropped on top of it, so that afterwards the two disks are rotating together at a new uniform angular velocity. How is the new angular velocity related to the old one?

Explanation / Answer

1.

F=ma ……………..Linear

= I ……………..Rotational

2.

I1=mr1^2

I2= mr2^2

But r2= 2r1

Hence

I2=mr2^2 = m(2r1)^2 = 4mr1^2= 4I1

Moment of inertia increases by 4.

3.

By law of conservation of angular momentum,

Iiwi=Ifwf

I1wi =(I1+I2)wf

I1wi =(I1+I1)wf

I1wi = 2I1wf

wf = wi/2

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