Conceptual Question (Rotational Kinematics)

[Dmt669]

A thin rod rotates at a constant angular spped. COnsider the tangential spped of each point on the rod for the case when the axis of rotation is perpendicular to the rod (a) at its center and (b) at one end. Explain for each case whether there are any points on the rod that have the same tangential speeds

This came from Cutnell and Johnson Physics 5th edition, does anyone know where I could find answer to their conceptual quesitons, math would be nice too ,thanks

 

[Andrew Mason]

A thin rod rotates at a constant angular spped. COnsider the tangential spped of each point on the rod for the case when the axis of rotation is perpendicular to the rod (a) at its center and (b) at one end. Explain for each case whether there are any points on the rod that have the same tangential speeds

This came from Cutnell and Johnson Physics 5th edition, does anyone know where I could find answer to their conceptual quesitons, math would be nice too ,thanks

Usually conceptual questions are answered by thinking about them. They test whether you understand the concepts. Finding answers from a source other than your mind defeats their purpose.

(Assume that the 'points' being referred to have a single co-ordinate being the distance from the axis of rotation). So the question is really asking, are there two locations on the rod that have the same tangential speed? Given that the rod has a constant angular speed, what determines tangential speed? To answer this you have to know the mathematical expression for tangential speed: how fast would an ant a distance d from the axis be moving if the rod is moving at constant angular speed $\omega$?

Then apply this to situations a) and b).

AM

 

[wais]

For the case when the axis of rotation is perpendicular to the rod, the tangential speed of each point on the rod will be constant. This is because all points on the rod are equidistant from the axis of rotation, and therefore will have the same angular velocity. However, the linear speed will vary depending on the distance from the axis of rotation.

(a) At the center of the rod, all points will have the same tangential speed since they are all the same distance from the axis of rotation. This is because the center of the rod is the point of rotation, so all points on the rod will have the same angular velocity and therefore the same tangential speed.

(b) At one end of the rod, the tangential speed will be different from the center. This is because the points closer to the end of the rod will have a larger linear speed compared to the points at the center. However, there will still be points on the rod that have the same tangential speed. For example, the points at the end of the rod and the points at the same distance from the axis of rotation on the other side of the rod will have the same tangential speed.

To find the answers to conceptual questions in Cutnell and Johnson Physics 5th edition, you can refer to the solutions manual or the end-of-chapter questions and answers section. For mathematical solutions, you can refer to the examples and practice problems in the textbook. Additionally, there are many online resources and study guides available for this textbook that may have further explanations and solutions to the conceptual questions.