Chapter 17 - Motion in a circle Flashcards
What is one radian?
The angle subtended by a circular arc with a length equal to the radius of the circle.
What is the equation for arc length?
l = rθ
How do you convert from degrees to radians?
Angle in degrees x π/180
What is circular motion?
The movement of an object along the circumference of a circle.
What is the period of circular motion?
The time taken for one complete revolution.
The instantaneous velocity is always ___________ to the radius of the circular path of an object.
The instantaneous velocity is always perpendicular to the radius of the circular path of an object.
An object in circular motion is accelerating due to _______ __________ _______. This acceleration is always acting towards the ______ __ ____ ________ _____.
An object in circular motion is accelerating due to changing instantaneous velocity. This acceleration is always acting towards the centre of the circular path.
An object is in uniform circular motion if…
… it is rotating at a steady rate.
What is angular displacement?
The angle an object in circular motion turns through.
What is angular speed?
The angular displacement per second.
What is the centripetal force?
The resultant force on an object moving around a circle at constant speed. It acts towards the centre of the circle.
What is the equation for angular velocity involving angular displacement?
ω = θ/t
ω = 2π/T = 2πf
What is the centripetal force acting on a car on a hill?
The resultant force of the weight of the car and the normal contact force (R) of the hill.
2
mv
—— = mg - R
r
What must happen for a car to lose contact with a hill?
What is the equation for speed required to do this?
The normal contact force of the hill must equal 0.
2
mv
R = mg - ——- = 0
r
2
v = gr
What is the centripetal force acting on a car around a roundabout?
The sideways friction between the car’s tyres and the road surface acting towards the centre of the roundabout.
What must be the case for no skidding or slipping to occur on a roundabout?
The force of friction must be less than the limiting force of friction (maximum value of friction (determined by weight of car)).
2 Limiting force of friction = mv
-----
r
What causes the centripetal force of a vehicle on a banked track?
The sum of the horizontal components of the normal contact force on each wheel of the vehicle.
2
mv
(N1 + N2)sinθ = —–
r
What is the equation for the condition for no sideways friction acting on a moving object on a slope?
It is:
2
v = grtanθ
