Unit 4: Motion in a circle Flashcards
What is uniform circular motion?
When an object rotates at a steady rate
What is the formula for frequency?
f = 1/T where T is the time for one rotation
What is the formula for velocity and how is it derived?
v = 2πr/T and it is derived through distance travelled which is the circumference/time taken for one rotation
How do you calculate the number of rotations in one minute?
Multiply the frequency of rotation by 60
What does an object in uniform circular motion turn through an angle of each second?
2π/T radians where T is the time for one complete rotation
What are the formulas for the angular displacement of an object in time t?
2πt/T or 2πft
What is angular speed defined as?
The angular displacement per second
What is the formula for angular speed?
ω = 2πf
What is ω measured in?
Radians per second
What is the formula for velocity in terms of ω?
v = rω
What is the formula for the length of an arc?
s = rθ
Why does an object accelerate when it is travelling in a circle?
The velocity of an object moving around a circle at constant speed continuously changes direction
What is acceleration?
The change of velocity per second
In which direction is the velocity of an object at any point in a circle?
Along the tangent to the circle at that point
Why is the acceleration towards the centre of the circle and what is this acceleration called?
The change in direction of the velocity is towards the centre of the circle therefore the acceleration is towards the centre of the circle and this type of acceleration is centripetal acceleration
What is the formula for centripetal acceleration in terms of v?
a = v^2/r
What is the formula for centripetal acceleration in terms of ω?
a = rω^2
What type of quantities are acceleration and velocity?
Vectors
In which direction does the acceleration of an object act?
In the same direction as the resultant force
What is the centripetal force referred to as and in which direction does it act?
The resultant force on an object moving round a circle at constant speed and it acts towards the centre of the circle
What are the formulas of the centripetal force?
F = mrω^2 or F = mv^2/r
How is the formula for centripetal force derived?
Through using Newton’s second law i.e. F = ma
What is required to make an object move round on a circular path?
It must be acted on by a resultant force which changes its direction of motion
Why is no work done by the centripetal force and what is the effect on kinetic energy?
This force is at right angles to the direction of the object’s velocity and there is no displacement in the direction of the force therefore the kinetic energy of the object is constant and so the speed is unchanged
What is the centripetal force for an object whirling around on the end of a string?
The tension in the string
What is the centripetal force for a satellite moving round the Earth?
The force of gravity between the satellite and the Earth
What is the centripetal force for a planet moving around the sun?
The force of gravity between the planet and the sun
What is the centripetal force for a capsule on the London Eye?
The centripetal force is the resultant of the support force on the capsule and the force of gravity on it
When using a magnetic field to bend a beam of charged particles, what is the centripetal force?
The magnetic force on the moving charged particles
What is required to make an object move on a circular path?
The object must be acted on by a resultant force which is always towards the centre of the curvature of its path
Why is a road banked?
To enable vehicles to drive round without any sideways friction on the tyres and on a banked track, the speed can be higher
What is the centripetal force on a road vehicle provided by without any banking?
Sideways friction between the vehicle wheels and the road surface
What can happen to a vehicle on a bend if the speed is too high?
The vehicle can slip outwards
What centripetal acceleration values can be dangerous to the average person?
Values of more than 2-3g
What is the angle in radians defined as?
The arc length divided by the radius of the circle
How many radians are there in a complete circle?
2π
What is another name for linear speed v?
Tangential velocity
What is the frequency of an object in circular motion?
The number of complete revolutions per second
What is frequency measured in?
Hz
What would happen if the centripetal force of an object travelling in a circle were removed?
The object would fly off at a tangent
Why do the particles in a cyclotron (a type of particle accelerator) have the same angular speed yet different linear speeds?
They have different linear speeds as their distances from the centre varies however they have the same angular speed as they all rotate through the same angle in the same time
