Further mechanics - Circular motion Flashcards
What is angular velocity?
The rate of change of the angle at the centre of the circle
What is the centripetal force, and what is its direction?
The resultant force towards the centre of the circle required to keep a body in uniform circular motion. It is always directed towards the centre of the body’s rotation. Centripetal force is always perpendicular to the direction of travel.
What are the requirements for uniform circular motion?
The linear speed is constant, the particle is constantly changing velocity (accelerating) and there is no tangential acceleration.
What is the relationship between the linear speed, radius and banking angle for a car travelling around a banked corner (or a conical pendulum)?
tan θ = v² / r.g
ideal case where friction is not required on the bank
What is the direction of friction on a banked corner where the linear speed of the vehicle increases?
A higher linear speed requires a higher acceleration and resultant force towards the centre of rotation (centripetal). So, a component of the friction must act down the slope.
In vertical circular motion, when is the maximum: acceleration, velocity? Why?
Both at the bottom because the kinetic energy is at a maximum and the gpe is at a minimum. (At the maximum height of the cycle ek-> gpe max making a ek min)
What forces do you account for in any circular motion?
ONLY CENTRIPETAL NOT TANGENTIAL
weight is not accounted for other than at the minimum and maximum vertical displacements (centripetal forces are vertical)
How do you solve for velocities after a period of time t of vertical circular motion?
Energy transfers Δgpe = Δek
When is the tension T a maximum?
At the minimum vertical height (the bottom of the cycle)
What happens as a car approaching a hump goes over it at a higher speed?
mg - N = mv² / r
Since mg does not change, but the value of the centripetal acceleration increases, the normal contact force will flip too negative (0) and the car will loose contact with the road.
