A disk of radius 25 cm is free to turn about an axle perpendicular to it through its center. It has a thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk, as shown in the figure below. The pull increases in magnitude, producing an acceleration of the ball that obeys the equation a(t) = At where A is a constant, and t is the time in seconds. The cylinder starts from rest, and after 3 seconds, the ball's acceleration is 1.8 m/s². Disk Ball Pull a) Find the value of the constant A b) Express the angular acceleration of the disk as a function of time c) How much time after the disk has begun to turn does it reach an angular speed of 15 rad/s d) Through what angle has the disk turned as it reaches 15 rad/s

A disk of radius 25 cm is free to turn about an axle perpendicular to it through its center. It has a thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk, as shown in the figure below. The pull increases in magnitude, producing an acceleration of the ball that obeys the equation a(t) = At where A is a constant, and t is the time in seconds. The cylinder starts from rest, and after 3 seconds, the ball's acceleration is 1.8 m/s². Disk Ball Pull a) Find the value of the constant A b) Express the angular acceleration of the disk as a function of time c) How much time after the disk has begun to turn does it reach an angular speed of 15 rad/s d) Through what angle has the disk turned as it reaches 15 rad/s

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 disk of radius 25 cm is free to turn about an axle perpendicular to it through its center. It has a
thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled
tangentially away from the rim of the disk, as shown in the figure below. The pull increases in
magnitude, producing an acceleration of the ball that obeys the equation a(t) = At where A is a
constant, and t is the time in seconds. The cylinder starts from rest, and after 3 seconds, the
ball's acceleration is 1.8 m/s².
Disk
Ball
Pull
a) Find the value of the constant A
b) Express the angular acceleration of the disk as a function of time
c) How much time after the disk has begun to turn does it reach an angular speed of 15 rad/s
d) Through what angle has the disk turned as it reaches 15 rad/s

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