16 - Circular Motion Flashcards
Define the radian.
The angle subtended by a circular arc with a length equal to the radius of the circle.
What is 360° in radians?
360° = 2π radians
How do you convert between radians and degrees?
Divide the angle by π.
What is angular velocity of an object in circular motion?
The rate of change of angle.
What is the frequency of an object in circular motion?
The number of rotations per unit time. (Hz)
What is the frequency of an object in circular motion?
The time taken to complete one rotation. (Seconds)
What are the two equations for angular frequency?
ω = 2πf
ω = 2π / T
What is the symbol for angular frequency
ω
What is the most commonly used unit for angular frequency?
rad s⁻¹
Radians per second
What does any object require in order to accelerate?
A resultant force to be acting on it.
What is centripetal force?
Any force that keeps a body moving with a uniform speed along a circular path.
In what direction does a centripetal force always act?
Perpendicular to the velocity of the object.
Towards the centre of the circle.
What would the centripetal force be in the following situations?
- Car going round a bend
- Satellite in orbit
- Yo-yo swung on a string
- Friction
- Gravity
- Tension
How do we calculate the velocity of an object in circular motion?
v = ωr
Speed = Distance / Time
One rotation: Distance = 2πr (Circumference)
Time = T (Period)
2πr / T --> ωr (ω = 2π / T)
What is the linear velocity at any instance proportional to?
v ∝ r
What is centripetal acceleration?
The acceleration of any object travelling in circular motion at a constant speed.
What direction does centripetal acceleration always act?
Perpendicular to velocity.
Towards the centre of the circle.
What are the two equations for centripetal acceleration?
a = v² / r
a = ω²r
What equation for force do we combine with an equation for centripetal acceleration to get centripetal force?
F = ma
What are the two equations for centripetal force?
F = mv² / r
F = mω²r
What happens if the centripetal force is not great enough?
The object does not follow circular motion and the radius of the circle will increase.
How do banked surfaces increase the velocity that vehicles can go round corners at?
It means that it is not just friction but a horizontal component of the normal contact force that provides centripetal force, meaning this is greater.
