6. A uniform circular disc of mass m and radius 2a . centre O, is smoothly pivoted at a point A,where OA=a.(i)Find the moment of inertia of the disc about an avis through A perpendicularto the plane of the disc.The disc is free to rotate in a vertical plane about the axis through A. Given thatthe disc is held with O directly above A and then slightly displaced so that it swingsin a vertical plane,(ii)show that in the ensuing motion,de3adt= 29(1 – cos0),%3Dwhere o is the angle AO makes with the upward vertical. (iii) Show further that when the disc has rotated such that AO makes an angle 0(m with the upward vertical, where 0,2(ln S)1 3at =COs Ccthall bu(iv) Find the reaction at the pivot when 0 = a.

The parallel axis theorem states that the moment of inertia about a new axis which is parallel to…

6. A uniform circular disc of mass m and radius 2a . centre O, is smoothly pivoted at a point A where OA=a. (i) Find the moment of inertia of the disc about an axis through A perpendicular to the plane of the disc.

6. A uniform circular disc of mass m and radius 2a . centre O, is smoothly pivoted at a point A where OA=a. (i) Find the moment of inertia of the disc about an axis through A perpendicular to the plane of the disc.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 63P: A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

6. A uniform circular disc of mass m and radius 2a . centre O, is smoothly pivoted at a point A,
where OA=a.
(i)
Find the moment of inertia of the disc about an avis through A perpendicular
to the plane of the disc.
The disc is free to rotate in a vertical plane about the axis through A. Given that
the disc is held with O directly above A and then slightly displaced so that it swings
in a vertical plane,
(ii)
show that in the ensuing motion,
de
3a
dt
= 29(1 – cos0),
%3D
where o is the angle AO makes with the upward vertical.

(iii) Show further that when the disc has rotated such that AO makes an angle 0
(m with the upward vertical, where 0,
2
(ln S)
1 3a
t =
COs Cc
thall bu
(iv) Find the reaction at the pivot when 0 = a.

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