A spool consists of a cylinder with two circular disks glued on either end. It has mass m, moment of inertia I, inner (cylinder) radius r, and outer (disk) radius R. String is wrapped tightly around the cylinder. The spool is placed on its side and the string is pulled with force T from an angle 0 above the horizontal. The spool rolls without slipping. (a) Compute the angular acceleration about the center of mass at the instant the force is first applied. (b) Which way does the spool roll, right or left? Does this depend on the properties of the spool and/or the angle 0? If so, find a formula. Note: if you did not succeed in part 1, you can still get partial credit here for a correct qualitative discussion.

A spool consists of a cylinder with two circular disks glued on either end. It has mass m, moment of inertia I, inner (cylinder) radius r, and outer (disk) radius R. String is wrapped tightly around the cylinder. The spool is placed on its side and the string is pulled with force T from an angle 0 above the horizontal. The spool rolls without slipping. (a) Compute the angular acceleration about the center of mass at the instant the force is first applied. (b) Which way does the spool roll, right or left? Does this depend on the properties of the spool and/or the angle 0? If so, find a formula. Note: if you did not succeed in part 1, you can still get partial credit here for a correct qualitative discussion.

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 spool consists of a cylinder with two circular disks glued on either end. It has
mass m, moment of inertia I, inner (cylinder) radius r, and outer (disk) radius R.
String is wrapped tightly around the cylinder. The spool is placed on its side and
the string is pulled with force T from an angle 0 above the horizontal. The spool
rolls without slipping.
(a) Compute the angular acceleration about the center of mass at the instant the
force is first applied.
(b) Which way does the spool roll, right or left? Does this depend on the properties
of the spool and/or the angle 0? If so, find a formula. Note: if you did not
succeed in part 1, you can still get partial credit here for a correct qualitative
discussion.

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