Motion in a Circle Flashcards
define angular displacement
the change in angle, in radians, of a body as it rotates around a circle
define a radian
the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle
is angular speed scalar or vector
scalar bcos…?
define angular speed
the rate of change of angular displacement, with respect to time
how can there be centripetal acceleration despite constant speed
an object in uniform circular motion is continuously changing direction and is therefore constantly changing velocity even though the speed is the same
explain the mechanics of centripetal acceleration using Newton’s first law
As Newtons 1st law states that ‘a body continues at rest or motion with constant speed in a straight line unless an external resultant force is applied (if EITHER condition is not satisfied then this is law is no longer obeyed)
Therefore this law justifies that ther IS a resultant force because in circular motion the body does NOT travel in a straight line.
The resultant force, which must be supplied by another force(/s) as it cannot exist on its own, is towards the centre and perpendicular to the linear speed because this is crucial in order to change only the direction while keeping the speed constant. (think of the box moving horizontally and a downward force is applied and it has no components horizontally hence no effect)
which law can be used to prove that both centripetal force and acceleration are in the same direction
Newton’s 2nd law
do centripetal force and accelerattion change
no they are constant
define centripetal acceleration
acceleration of an object towards the centre of a circle when an object is in motion (rotating) around a circle at a constant speed
object moving in a circle in a circle is not in equilibrium therefore has a _, which is required to …
resultant force ie the centripetal force (its not a seperate force of its own, though)
needed to keep the object in uniform circular motion
What is the formula of angular displacement
🔺️Ø=🔺️S / r
Angular displacement/ angle of rotation = length of arc/distance travelled around circle / radius
How to convert Ø to rad?
Ø × pi/180
Formula for angular speed where angular displacement is a complete cycle
w=🔺️Ø/🔺️t
w= 2pi/T= 2piF (cos 1/T=F)
Formula for angular velocity when an object travels ar a constant linear speed (derivation)
w= v/r
3 formulae of centripetal acceleration
a= v^2/r a= rw^2 a= vw
