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Revision:Motion Of A Rigid BodyTSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Motion of a Rigid Body These notes are based on the requirement of the M5 A Level mathematics module.
Rotation of a rigid body
Moment of the resultant force about an axis:
To find the force that the body is doing on the axis: put force X at the axis in the direction GO, and force Y at O perpendicular to OG. Then resolve any other forces on the body in the directions OY and OX, then use:
hence find X and Y, and then find their resultant force (if required to find the magnitude of the force acting on the axis).
Angular momentumAngular momentum = moment of momentum (How to derive that is in the same book page 94, also contact me if needed.)
Conservation of angular momentumSame as conservation of momentum, angular momentumbefore = angular momentumafter
ExampleA rod ( mass m, length 4a ) is free to rotate about a vertical axis through its centre, it rests on a smooth horizontal table, a particle of mass 3m moving in a straight line perpendicular to the rod with speed u ms[sup]-1[/sup] hits the rod at distance a from one of its ends. The particle sticks to the rod. Find the angular speed of the body after collision.
Initial angular momentumparticle
Final angular momentumparticle
Effect of an Impulse on a rigid body that is free to rotate about an axisYou know that:
usually
PendulumsSimple pendulum
Compound pendulum
where h is the distance between axis and C.M. and I is moments of inertia about the axis.
where k is the radius of gyration.
i.e.
CommentsOriginally written by yazan_l on TSR forums. |
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![\displaystyle \int_{t_1}^{t_2} L\ dt = [I \theta’]_{\omega_1}^{\omega_2}](http://www.thestudentroom.co.uk/latexrender/pictures/ae/ae0640043014e306f192c82d9633519e.png "\displaystyle \int_{t_1}^{t_2} L\ dt = [I \theta’]_{\omega_1}^{\omega_2}")
