Help quite hard pendulum problem

[charmedbeauty]

Homework Statement

A very light rigid rod with a length of 0.062 m extends straight out from one end of a metre stick. The combination is suspended from a pivot at the upper end of the rod as shown in the following figure. The combination is then pulled out by a small angle and released.

Homework Equations

The Attempt at a Solution

well using parallel axis Theorem

I= 1/12mL²+md²

ω=√mgd/I

T=2∏/ω

T=2∏√(I/mgd)

= 2∏√((1/12)(m)(L)²+md²)/mgd

m's cancel

=2∏√((1/12)(L)²+d²)/gd

but what should d be??

is it a half L, I'm confused

is this the right method as well?

 

[tiny-tim]

hi charmedbeauty!

A very light rigid rod with a length of 0.062 m extends straight out from one end of a metre stick. The combination is suspended from a pivot at the upper end of the rod as shown in the following figure.
…
but what should d be??

is it a half L, I'm confused

is this the right method as well?

looks ok

you're using the parallel axis theorem, and your axis through the c.o.m. is perpendicular to the rod, so d is the perpendicular distance from that axis to the pivot, ie the distance PC from the pivot P to the c.o.m. C

(if you're wondering how the moment of inertia can be the same whatever the angle θ of the stick, just do a bit of geometry using the cosine formula for two points A and B on the stick equidistant from C … you'll find that PA² + PB² is independent of θ )

 

[charmedbeauty]

hi charmedbeauty!


looks ok

you're using the parallel axis theorem, and your axis through the c.o.m. is perpendicular to the rod, so d is the perpendicular distance from that axis to the pivot, ie the distance PC from the pivot P to the c.o.m. C

(if you're wondering how the moment of inertia can be the same whatever the angle θ of the stick, just do a bit of geometry using the cosine formula for two points A and B on the stick equidistant from C … you'll find that PA² + PB² is independent of θ )

so say I have the pivot point which is connected to a rod which in turn is connected to a ruler then d would be the length of the the rod+half that of the ruler?? i.e. 0.5+0.062=d

http://www.webassign.net/serpse8/15-p-034-alt.gif

thats the pic there with all details given in question.

 

[tiny-tim]

so say I have the pivot point which is connected to a rod which in turn is connected to a ruler then d would be the length of the the rod+half that of the ruler?? i.e. 0.5+0.062=d

(oh it's straight!)

yes

 

[charmedbeauty]

(oh it's straight!)

yes

Thanks a bunch tiny-tim

 

[charmedbeauty]

Thanks a bunch tiny-tim

and just to double check L is the length of the rod (0.062) and not the length of the ruler?

 

[tiny-tim]

no, L is in 1/12 mL² …

L is the length of the thing that has mass m (in this case, the metre stick)

 

[charmedbeauty]

no, L is in 1/12 mL² …

L is the length of the thing that has mass m (in this case, the metre stick)

oh right so I can just leave it out since it is 1 metre. cool.