Question

QUESTION 1:

Two point masses are the same distance R from an axis of rotation and have moments of inertia I_A and I_B.

(a)

If I_B = 4I_A, what is the ratio

mB

mA

of the two masses?

mB

mA

=

(b)

In terms of R, at what distance from the axis of rotation should mass A be placed so that

I_A = I_B?

R

QUESTION 2:

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 230 N applied to its edge causes the wheel to have an angular acceleration of 0.980 rad/s².

(a) What is the moment of inertia of the wheel?
kg · m²

(b) What is the mass of the wheel?
kg

(c) If the wheel starts from rest, what is its angular velocity after 4.60 s have elapsed, assuming the force is acting during that time?
rad/s

Answer 1

ANSWER 1:

The moment of inertia of a point mass is given by

PART A:

Moment of inertia of two masses are

We know

Putting the value of I_A into the above equation

So, the ratio is 4.

PART B:

Now, we have

But we have different masses given by

We have

and

Both are equal. i.e

Putting the value of m_B

Assuming B is placed at R

So, mass A is placed at a distance 2R from the axis of the rotation.