Motion in a Circle Flashcards
Angular displacement
the change in angle, in radians, of a body as it rotates around a circle
Equation of angular displacement
△ θ = △s / r
Radian
the angle subtended at the center of the circle by an arc equal in length to the radius of the circle
To convert from degrees to radians, and from radians to degrees
degrees to radians: multiply by 2 π/360 or π /180
radians to degrees: multiply by 360/2 π or 180/π
Angular speed
the rate of change in angular displacement with respect to time
Equation for angular speed
ω = △ θ / △t
Considering an object with a single revolution: ω = 2pi / T
ω directly proportional to △ θ
ω directly proportional to 1 / r
Explain centripetal force
Newton’s first law states every object will remain at rest or in uniform motion in a straight line unlees axted upon a resultant force
In the case of an object moving at steady speed in a circle, we have a body whose velocity is not constant. Hence, there is a resultant force acting on it.
Centripetal force, and therefore, centripetal acceleration, act in the same direction, PERPENDICULAR to its velocity
Why is speed constant in circular motion, despite having a resultant force?
Because centripetal force is 90° / perpendicular to direction of velocity
Changing speed requires a component in the direction of velocity
In terms of work done, W = Fd. The distance (d) moved by the object in direction of force is 0. Hence, no work is done and Ek remains the same.
Centripetal acceleration
the acceleration of an object towards the centre of the circle when an object is rotating around the circle at a constant speed
Equation for centripetal acceleration
a = v^2 / r
a = r ω^2
Centripetal force
the resultant force towards the centre of the circle requires to keep a body in uniform circular motion, always directed towards the centre of the body’s rotation
Equation for centripetal force
F = mv^2/r = mr ω^2 = mv ω
