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A thin, straight, uniform rod of length $\ell=1.00 \mathrm{m}$ and mass $m=215 \mathrm{g}$ hangs from a pivot at one end. $(a)$ What is its period for small-amplitude oscillations? (b) What is the length of a simple pendulum that will have the same period?

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a. $$1.64 \mathrm{s}$$b. $$0.67 \mathrm{m}$$

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

05:16

A rigid rod of length L= m…

01:20

A uniform rod of length $l…

03:52

A very light rigid rod wit…

04:52

03:23

A physical pendulum consis…

08:17

A small ball of mass $M$…

01:12

A grandfather clock keeps …

06:52

A pendulum is made from a …

01:50

05:44

A pendulum clock keeps tim…

01:13

Consider a simple pendulum…

07:10

A very light rigid rod of …

02:46

A pendulum of length $L$ a…

so here to find the period of a physical pendulum. This is going to equal to pi times that the moment of inertia divided by MGH So this will equal to pi times the square root of 1/3. Um, I'll squared and this is gonna be divided by M g times 1/2 of l. So this is gonna equal to pi times to AL over three g and we can solve. So the period is gonna be equal to two pi times the square root of two times one meter being the length divided by three times 9.8 meters per second squared being the acceleration due to gravity. And we find that the period of this pendulum is going to be 1.64 seconds. So this would be your final answer for a party and then for part B, we're going to relate the formula above to a simple pendulum to find length. So t is equaling two pi times the square root of all over G. This would be the formula for the This would be the formula for these simple pendulum, and this is gonna equal to pi times to our over three g. So at this point, we know that the length of the simple pendulum would be equal to two out over three. Or we could just say 0.667 So two times one, remember three. So l simple, but vehicle 2.667 Yeah, meters, This'd be our final answer. That is the end of the solution. Thank you for watching.

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