Physics-Rotational motion and astrophysics

what does the gradient of a curve/ straight line on a motion time graph represent and how can this be calcuclated?

this represents instantaneous rate of change and can be calculated through differentiation

what does the gradient of a curve/straight line on a displacement-time graph represent?

instantaneous velocity

what does the gradient/curve on a velocity-time graph represent?

instantaneous acceleration

what is velocity

rate of change of displacement with time

what is acceleration?

the rate of change of velocity with time

what is acceleration? (differentiation)

the second differential of displacement with time

how can the area under a line on a graph be calculated?

intergration

why is a centripetal (radial or central) force acting on an object necessary?

it maintains circular motion and results in centripetal acceleration of the object.

I=1/2ml² is to calculate the moment of inertia of what?

rod about the centre

I=1/3ml² is to calculate the moment of inertia of what?

rod about the end

I=1/2mr² is to calculate the moment of inertia of what?

disc about the centre

I=2/5mr² is to calculate the moment of inertia of what?

sphere about the centre

what does moment of inertia depend on?

mass and distribution of a mass about a given axis of rotation

what is moment of inertia of an object?

A measure of an object's resistance to changes in its rotational motion, depending on the mass distribution relative to the axis of rotation.

how to turn something into light years

x 60 × 60 × 24 × 365.25

what is gravitational potential of a point in space?

the work donw in moving unit mass from infinity to that point.

the energy to move mass between two points in a gravitational field is independent on what?

the path taken between points