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36 Cards in this Set
- Front
- Back
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The angular momentum of a system is conserved when... |
There is no net torque |
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When is rotational mechanics analogous to Linear mechanics |
Rotation about an axis of symmetry |
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What is the conventional direction of a spinning disc |
Anticlockwise is positive |
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Define centre of mass |
A mass weighted average position of the particles |
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Give a property when finding the centre of mass of an extended object |
Uniform density |
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Three steps for finding the centre of mass for an extended object |
Find DM Find the relationship between l and X (area or volume) Substitute into equation ) Substitute into equation |
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An objects moment of inertia depends on... |
It's axis of rotation |
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What are the units of moment of inertia |
KgM^2 |
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Formula for the total energy of a spinning object |
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What is a moment of inertia |
It tells us how hard it is to rotate an object |
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What is the total formula for inertia? |
Top equation |
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What is the parallel axis theorem? |
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What is the difference between the centre of mass and inertia integrals? |
com integrates x, whereas inertia integrates x^2 and does not have 1/M before the integral |
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Total kinetic energy is the summation of... |
Translation KE and Rotational KE |
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The ability of a force to cause rotation depends on three factors...? |
The magnitude of the force The distance r from the point of application to the pivot The angle at which the force is applied |
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Formulae for torque, and at what angle it is measured... |
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2 conditions for a rigid body to be in total equilibrium |
No net torque No net force |
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The kinetic energy of solely rolling is due to... |
Kinetic energy of both rotation and translation |
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2 Formulae for angular momentum |
L=rxp for a particle L=iw for a rigid body |
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Give an alternative formula for rxp for angular momentum |
mrvsin(beta) |
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The angular momentum vector and angular velocity vector will on point in the same direction when... |
Rotation of a symmetrical object is rotating about the symmetry axis |
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Is it easy or hard to change the vector L in this situation, and why? |
Hard, as a large torque is required to change the direction of L |
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The formula for rotational work is |
dW=T(theta) |
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Total rotational work is |
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Rotational power is |
P=dW/dt |
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The final angular velocity is given by |
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The final angle theta is given by |
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The final angular velocity squared is given by |
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Tangential acceleration is given by |
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Radial acceleration given by |
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The angular momentum of a gyroscope can only change in the direction of |
The torque vector |
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As the angular velocity of a spinning disc decreases does the gyroscope precess faster or slower |
Faster, as d(theta) /dt increases |
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Why does a torque cause a change in direction? |
The torque cannot alter the rotation speed at the disk, so the magnitude of L remains constant. However in a time dT the angular momentum vector Changes by tau*dt and this results in a change in the direction. |
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A use for gyroscopes |
Gyrostabilizer in ships. It uses a large gyroscope to reduce roll on ships by making necessary a large torque to alter L |
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The work done is also the |
Change in Rotational kinetic energy |
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Linear velocity |
V=angular velocity * r |
