Rotational dynamics Flashcards
What is inertia?
The resistance to a change of motion in linear motion
The larger the mass of an object, the greater the inertia
What is the moment of inertia?
The rotational equivilant of inertia for linear motion
The resistance to a change of rotational motion, depending on the distribution of mass around a chosen axis of rotation
What does the moment of inertia measure?
How ‘easy’ or ‘hard’ it is to rotate an object
How do you calculate moment of inertia when a system has more than one component rotating the same axis?
We calculate the moment of inertia of each individual component seperately, using their individual mass and radius, and then add it together for the overall moment of inertia
How do you calculate moment of inertia?
Moment of inertia = mass x radius^2
Why do we need moment of inertia?
The moment of inertia in rotational dynamics plays the same roll as mass in linear motion
Instead of using mass in equations, we use moment of inertia
What is rotational kinetic energy?
A body moving with linear motion has an associated linear kinetic energy. Similarily, a rotating object has an associated rotational kinetic energy
How do you calculate rotational kinetic energy?
It is given by its moment of inertia (in place for mass) and angular velocity (in place for velocity)
Rotational kinetic energy = 1/2 x moment of inertia x angular velocity^2
What is rolling motion?
Circular objects are made to move with both linear and rotational motion
Rolling motion is a combination of rotating and sliding (tranational) motion
How does angular and linear velocity differ as a disc rotates?
Each point on the disc has a different angular velocity depending on its distance from the centre
The linear velocity is the same at all points on the circumference
What happens when a disc rolls without sliping?
There is enough friction present to initiate rotational motion
The point in contact with the surface has a velocity of 0
The centre of mass has a velocity of angular velocity x radius
The top point has a velocity of angular velocity x radius^2
What happens to GPE when rolling down a slope?
As the object rolls down the slope, the gravitational potential energy is transferred to both the linear (translational) kinetic energy and rotational kinetic energy as 2 seperate stores
