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epsc 200 chapter 7 notes.docx

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McGill University
CHEM 222
Karine Auclair

7. Rotational Dynamics of the Planets and their Satellites - Planets rotate on their own axes (as do the moons of the planets) - The Earth wobbles as it rotates • Partly due to the seasonal movement of mass over the Earth (seasonal wobble) - The Moon librates (swings back and forth) as it orbits the Earth Key Points: - Jupiter rotates fastest - Venus rotates slowest - Venus, Uranus, and Pluto are inclined more than 90 to their orbital plane. - Pluto and Uranus rotate with their axes lying almost in their orbital plane - Venus has highest inclination angle (it rotates backwards in relation to its revolution about the Sun 7.1 Moments of Inertia of the Planets - A rotating body tends to stay in rotation unless acted upon by an external torque. - Angular Momentum ( ) = The quality and quantity which determines the continuing tendency to rotates - Rate of Rotation ( ) = In radians, determines the number of turns per unit time (rad/s) - If we look at the example of a spinning bicycle wheel, we find that (angular momentum – the tendency of the wheel to keep spinning) is proportional to the radius of the wheel (a), the mass of the wheel (m )wand the rate of rotation ( )  m w 2  a  - The properties inherent to the wheel are assembled as the moment of inertia (its inertia with respect to rotational motion) of the wheel: 2 2 I = m w a (mass x radius ) - The angular momentum of the spinning wheel is: L = I  - If we can determine I for a planet, we can learn something useful about how mass or density is distributed within • Perfectly spherical2planet of uniform density - I = (2/5)(ma ) • Perfectly spherical planet with mass concentrated in thin surface layer - I = (2/3)(ma )2 • Perfectly spherical planet with all mass concentrated at its centre - I = 0 - The lower the moment of inertia, the more concentrated the mass it at the centre. 2 - I < 0.4ma  mass concentrated towards centre - I = 0.4ma  uniform density - I > 0.4ma  mass concentrated towards surface - The lower the moment of inertia, the more mass is concentrated at the depth. 7.2 Determining I by Astronomic Observations - We can neither brake nor accelerate the rotation of a planet in order to measure its moment of inertia – this can be determined by observing a planet’s response to astronomical forces and torques. - Inertial space = background reference (frame of reference) provided by the phenomenon of inertia) - When a body rotates on an axle, it maintains its angular momentum vector fixed in inertial space • The axis of rotation (the centre around which the Earth spins) orbits the Sun in an ellipse. • The axis of rotation is fixed in inertial - Torque = The angular force that causes a change in rotation. • Torque is the force that is, at a distance, applied to the axis of rotation - When a torque is applied to the axle, a reactive torque exactly 90 to applied torque results in maintaining torque balances. - The Moon applies a twisting torque to the axle upon which the Earth rotates – the reaction torque causes the Earth’s axis to move in a direction 90 to the applied torque. - The Earth is a slightly flattened ellipsoid (it’s equatorial radius is greater than its polar radius) - The Moon’s present location is not aligned with the equator of the Earth. - On the side that is closer to the moon, there is a great
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