circular motion Flashcards
define angular displacement
It is the angle an object makes with respect to a reference line
what is defined by a radian
It is the angle subtended by an arc length that is equal to the radius of the arc
what is the formula to find theta
theta= s/r
define angular velocity, w
it is the rate of change of angular displacement with respect to time
define the period of an object in circular motion
It is defined as the time taken for an object to make one complete revolution
define the frequency of an object in circular motion
it is the number of revolutions made by an object per unit time
express linear velocity as an expression of angular velocity
v= rw
derived from differentiation of the eqn s=r theta with respect to t, where r is a constant
explain the relationship between angular velocity and frequency and period
w= 2pie/T
w= 2pie * f
explain the relationship between linear velocity and period T
T= (2pie * r) /v
what are the 3 formulas for centripetal acceleration
a= vw
a= rw^2
a= v^2/r
is there work done on an object in circular motion
there is no work done as there is no displacement in the direction of motion of the object.
how do you solve circular motion questions
- draw free body diagram
2.resolve into horizontal and vertical components - Equate components to the centripetal forces where possible
- solve
how do you find out the minimum speed to reach the top of a loop in non uniform circular motio
let the normal contact force at the top be 0
0+mg = mv^2/r
mg = mv^2/r
v^2/r=g
v = sqr root rg
how do you find out the maximum bottom speed such that the loop is completed
by law of conservation of energy
energy at bottom = energy at top
1/2mv^2 = 1/2 mv top min ^2 +mgh
1/2mvbottom^2 = 1/2 mgr + mg(2r)
v bottom = sqr root 5gr
