Two identical light rods

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

Two identical light rods, each of length

40\,\text{cm}

, are joined at right angles to form an L-shaped frame that can rotate about a vertical axis through the common junction

O

. Three small lead shots, each of mass

0.10\,\text{kg}

, are soldered to the frame as follows: • Shot

A

at the free end of the first rod • Shot

B

at the free end of the second rod • Shot

C

somewhere on the first rod between

O

and shot

A

The moment of inertia of the system about the vertical axis through

O

is required to remain unchanged when shot

C

is removed and a new shot

D

of mass

0.15\,\text{kg}

is fixed on the second rod between

O

and shot

B

. (i) Taking

x

to be the distance of shot

C

from

O

and

y

the distance of shot

D

from

O

, obtain an expression equating the two moments of inertia before and after the replacement. (ii) If

x = 0.20\,\text{m}

, calculate

y

. (iii) Comment on whether the centre of mass of the system shifts closer to or farther from the axis after the replacement, giving one supporting calculation.

Related theory

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