Rotational motion Flashcards
velocity and acceleration definitions
velocity-the rate of change of displacement
acceleration-the rate of change of velocity
what does the gradient of a velocity-time diagram give?
the value of acceleration
(for non-constant graph->gradient of tangent=instantaneous a->found by differentiating)
what does the area of a velocity-time graph give?
total displacement
(for a non-constant graph, you must integrate to find this)
what does the area under an acceleration-time graph give?
the overall change in velocity (found by integrating the equation of graph)
What happens if angular velocity is constant?
angular acceleration and tangential acceleration are 0
Which accelerations are 90degrees to each other?
tangential acceleration and centripetal acceleration
what is centripetal acceleration?
It is required to change the direction of an object in circular motion-it is a vector which always points to the centre of a circle
What is centripetal force?
A centripetal force acting on an object is necessary to maintain circular motion and results in centripetal acceleration of an object
NOT a real force unlike friction and tension
Forces when whirling in a horizontal circle
weight (downwards) and tension (inwards)
Fc=T (as it is the only force acting towards the centre)
Forces when whirling in a vertical circle
When ball is at top: Fc=T+W
When ball is at the side: Fc=T
When ball is at the bottom: Fc=T-W
Conical pendulum/banked track formulas
(T for conical, R for banked)
Fc=Tsinx
mg=Tcosx
for when we want to find angle and have no T:
tanx=Tsinx/Tcosx=mw^2r/mg=w^2r/g=v^2/gr
when does Fc=mg?
when centripetal acceleration=g (acceleration due to gravity)
Aircraft banking explanation
In order to turn, aircraft must fly ‘sideways’ so that they introduce a component of lift force acting inwards. This is what provides the centripetal force.
In rotational dynamics, what does an unbalanced torque produce?
an angular acceleration
Rolling objects:conservation of energy formula
Ep=Ek(translational)+Ek(rotational)
hollow v solid cylinder explanation
-moment of inertia of hollow cylinder is greater->Ek(rotational) is greater
-linear Ek must be smaller (total energy conserved)->smaller velocity
Solid cylinder reaches bottom first
Why does a mass accelerate when moving at a constant speed in a circle?
there is a centripetal force acting so the directing changes which means the velocity changes
If the speednof a sphere, moving ina. circular path, is reduced until it is no longer a circular path. Hwy is it no longer circular?
1-the tension reduces (to 0)
2-weight is greater than the centripetal force that would be required for circular motion
If the speednof a sphere, moving ina. circular path, is reduced until it is no longer a circular path. Hwy is it no longer circular?
1-the tension reduces (to 0)
2-weight is greater than the centripetal force that would be required for circular motion
