1999 Paper 3 Q11

Year: 1999
Paper: 3
Question Number: 11

Course: zNo longer examinable
Section: Moments of inertia

Difficulty: 1700.0 Banger: 1500.0

moments of inertia circular motion hoop parallel axis theorem energy conservation loss of contact rolling without slipping normal force rigid body rotation

Problem

Calculate the moment of inertia of a uniform thin circular hoop of mass \(m\) and radius \(a\) about an axis perpendicular to the plane of the hoop through a point on its circumference. The hoop, which is rough, rolls with speed \(v\) on a rough horizontal table straight towards the edge and rolls over the edge without initially losing contact with the edge. Show that the hoop will lose contact with the edge when it has rotated about the edge of the table through an angle \(\theta\), where \[ \cos\theta = \frac 12 +\frac {v^2}{2ag}. \] %Give the corresponding result for a smooth hoop and table.

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

Difficulty Comparisons: 0

Banger Rating: 1500.0

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Problem source

Calculate the moment of inertia of a 
uniform thin
 circular hoop of mass $m$ and radius $a$ about an axis perpendicular to the 
plane of the hoop through a point on its circumference.
The hoop, which is rough,  
rolls with speed $v$ on a rough  horizontal
table straight towards the edge and rolls over the edge without initially 
losing contact with the edge. Show that the hoop will lose contact with
the edge when it has rotated about the edge of the table
through an angle $\theta$, where
\[
\cos\theta = \frac 12 +\frac {v^2}{2ag}.
\]
%Give the corresponding result for a smooth hoop and table.

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