Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(II) A uniform thin rod of length $\ell$ and mass $M$ is suspended freely from one end. It is pulled to the side an angle $\theta$ and released. If friction can be ignored, what is angular velocity, and the speed of its free end, at the lowest point?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\sqrt{\frac{3 g}{\ell}(1-\cos \theta)}$, $\sqrt{3 g \ell(1-\cos \theta)}$

Physics 101 Mechanics

Chapter 10

Rotational Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

University of Michigan - Ann Arbor

Hope College

McMaster University

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

03:08

A thin, uniform rod of len…

02:29

04:22

01:30

A uniform thin rod of leng…

06:47

A uniform thin rod of mass…

01:48

A uniform rod of mass $M$ …

04:36

A uniform slender rod $A B…

02:45

A uniform rod of length $2…

01:33

13:15

One end of a thin, uniform…

02:46

(II) A uniform horizontal …

02:38

Thin Rod of length $L$ A t…

00:58

A thin uniform rod of leng…

04:02

$\cdots$ A thin, uniformlr…

So let's draw a diagram of the system. Uh, we can draw as a horizontal axis here and from this distance to hear this would be considered all over too. From this distance to this distance, this is Al over too. Again, this is not drawn to scale. We haven't angle here theta. And we can say from this distance to this distance, this would be l over two times one minus co sign of data. Uh, and we know that here mechanical energy is going to be conserved. So this means that the total kinetic energy would be equal to the rotational energy and this would equal 1/2 I omega squared. So we can say that initial equals e final due to the conservation of mechanical energy in this case, therefore, the initial potential energy would be equal to the final kinetic energy so we can say and G 1/2 of l times one minus co sign of theta. So that would essentially be the height. And this would be for the gravitational potential energy. This would be equal to 1/2 times the moment of inertia times the angular velocity at the bottom squared and we're going to use the moment of inertia for a Rod rotating about one end. So the moment of inertia of a Rod motor rotating about one end, this would be, Ah, 1/3 um, I'll squared. And then again, times the omega squared the angular velocity at the bottom. Therefore, the angular velocity at the bottom ah would be equal to the square root of three G over l times one minus co sign of fada. And the linear velocity at the bottom would simply be equal to the angular velocity at the bottom times the length of El. Therefore, the lean your velocity at the bottom would be equal to the square root of three G l one minus co sign a theater. So this would be the formula for the linear velocity and the formula for the angular velocity that is the end of the solution. Thank you for watching

View More Answers From This Book

Find Another Textbook

04:01

An 8-pole lap wound DC generator has 120 slots having 4 conductors per slot.…

01:23

Question # 01: A piece of RG-59B/U Coaxial cable has a nominal capacitance o…

03:40

Calculate circular convolution of the numbers 2091 and 6324.

01:18

The resistance of a certain aluminum power line is 150 Ω at 200 Find the…

02:30

Alice, Bob and Chuck are three friends standing around talking.We know t…

03:30

The radius of the earth’s orbit around the sun (assumed circular) is 1.50 x …

01:03

(a) The star Dubhe emits radiation with a peak wavelength of 622 nm. Wha…

03:03

Two light sources are used in a photoelectric experiment to determine the wo…

01:40

What is the source of self-inductance and back emf in a current-carrying loo…

02:31

CapacitanceA 40 µF capacitor with an air gap of 2 mm is connected across…