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(III) An ant crawls with constant speed outward along a radial spoke of a wheel rotating at constant angular velocity $\omega$ about a vertical axis. Write a vector equation for all the forces (including inertial forces) acting on the ant. Take the $x$ axis along the spoke, $y$ perpendicular to the spoke pointing to the ant's left, and the $z$ axis vertically upward. The wheel rotates counterclockwise as seenfrom above.

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Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

University of Winnipeg

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.

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

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04:22

(III) Show that the veloci…

it could be that diagram of the system for the aunt and this diagram is a view from above the wheel. We know that the aunt is moving in a curved path. So essentially, there's a fictitious outward radio force. Um, we can say m Omega squared. Are I had that would be this. This would be the outward radio force. Ah, we have a, uh the answer is moving away from the axis of rotation. So essentially, there is a Coriolis force right here. Um, and then the ant is moving with the constance feet speed. So in the rotating reference frame, the net force is going to be equaling zero Newton's, um, we know that the ah, the aunt is in contact with the spoke, so they're actually components of that contact force, a frictional force. And we also have this spoke, pushing in the opposite direction to the to the Coriolis Force. So we have a force of the smoke times J hat, so that would be here. Forcible spoke. And then in the ah, in the vertical direction, we know that there is gravity s. So we have a force of gravity. This would be of course. Negative mg. Okay. Huh? This is, of course, our X and Y Cartesian access. So we can't truly represent that on, um, on the graph, But this would be in essentially in the Z direction. And then there's the normal force, of course, F and K hat. And so these, uh, these we can say that the force of the rotating frame. If we were to then add these. This would be equaling two. I am Omega Squared, R minus the force of friction. I had this would be plus the force of the spoke minus two times M Omega V J hat plus And then, of course, forced Normal in the Z direction. Forced normal, minus mg times K hat. And so this would be our final answer. That is the end of the solution. Thank you for once.

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