mass, mass m, and radius r has a string wrapped around it which is tied to the ceiling (Figure 1). The cylinder's vertical position as a function of time is y(t). At time t = 0 the cylinder is released from rest at a height h above the ground. Figure < 1 of 1 The string constrains the rotational and translational motion of the cylinder. What is the relationship between the angular rotation rate w and v, the velocity of the center of mass of the cylinder? Remember that upward motion corresponds to positive linear velocity, and counterclockwise rotation corresponds to positive angular velocity. Express w in terms of u and other given quantities. ► View Available Hint(s) W = Submit | ΑΣΦ Part B Complete previous part(s) Part C ?

mass, mass m, and radius r has a string wrapped around it which is tied to the ceiling (Figure 1). The cylinder's vertical position as a function of time is y(t). At time t = 0 the cylinder is released from rest at a height h above the ground. Figure < 1 of 1 The string constrains the rotational and translational motion of the cylinder. What is the relationship between the angular rotation rate w and v, the velocity of the center of mass of the cylinder? Remember that upward motion corresponds to positive linear velocity, and counterclockwise rotation corresponds to positive angular velocity. Express w in terms of u and other given quantities. ► View Available Hint(s) W = Submit | ΑΣΦ Part B Complete previous part(s) Part C ?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

A cylinder with moment of inertia I about its center of
mass, mass m, and radius r has a string wrapped
around it which is tied to the ceiling (Figure 1). The
cylinder's vertical position as a function of time is y(t).
At time t = 0 the cylinder is released from rest at a
height h above the ground.
Figure
GO
1 of 1
Part A
The string constrains the rotational and translational motion of the cylinder. What is the relationship between the
angular rotation rate w and v, the velocity of the center of mass of the cylinder?
Remember that upward motion corresponds to positive linear velocity, and counterclockwise rotation corresponds to
positive angular velocity.
Express w in terms of u and other given quantities.
View Available Hint(s)
W =
ΠΑΠ ΑΣΦ
Submit
Part B Complete previous part(s)
Part C
?

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