Circular Motion Flashcards
Why is an object in uniform circular motion with a constant linear speed always accelerating
It has a continuously changing direction.
Velocity is the speed in a given direction therefore has a constantly changing velocity
The object must therefore be accelerating as acceleration is the rate of change of velocity
What is the acceleration of an object in uniform circular motion called and in what direction does it act
It is called centripetal acceleration
It is perpendicular to the direction of the linear speed and always acts towards the centre of the circle
What is the direction of velocity
At a tangent to the circle
What direction is the centripetal force in
The same direction as the acceleration, always towards the centre of the circle.
They are in the same direction because of Newton’s Second Law : F=ma
This shows that force is directly proportional to acceleration
What is centripetal acceleration caused by
A centripetal force of constant magnitude that also acts perpendicular to the direction of motion (towards the centre)
Angular displacement of a body in circular motion
The change in angle, in radians, of a body as it rotates around a circle
What is angular displacement the ratio of
Distance travelled around the circle : Radius of the circle
Radian
The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle
Equation for angular displacement (theta) in relation to the arc length and radius of the circle
theta = arc length / radius
Angular velocity (w) of a body in circular motion
The rate of change in angular displacement with respect to time
Units for angular velocity
rad / s
Equation linking angular velocity, time and theta
angular velocity = theta / Time
Equation linking angular velocity, linear velocity and radius of the circle
angular velocity = linear velocity / radius
Equation linking angular velocity, 2pi and frequency / time period
angular velocity = 2pi x frequency
OR
angular velocity = 2pi / Time period
Centripetal acceleration
The acceleration of an object towards the centre of a circle when an object is in motion/rotating around a circle at a constant speed
Equation linking acceleration, linear speed and radius
centripetal acceleration = linear speed ^2 / radius
Why is an object moving in a circle not in equilibrium
It has a resultant force acting on it - the centripetal force.
This force keeps the object moving in a circle
Centripetal force
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
What is the centripetal force for a car travelling around a roundabout
Friction between car tyres and the road
What is the centripetal force for a ball attached to a rope and moving in a circle
Tension in the rope
What is the centripetal force for the Earth orbiting the Sun
Gravitational force
Why is the kinetic energy of a particle moving in a circle with uniform speed constant
KE = 1/2 x m x v^2
Only the direction of the velocity changes, not the magnitude. Only the magnitude matters in this equation.
A ball is swung around on the end of a string so that the ball moves in a horizontal circle.
Discuss the motion of the ball in terms of the forces that act on it.
Explain how Newtons Laws apply to its motion in a circle
Explain why the string will not be horizontal
1st law :
Ball does not travel in a straight line so a force must be acting on it.
Although the ball has a constant speed its velocity is not constant as its direction is constantly changing.
Because its velocity is changing, it is accelerating
2nd law:
Force on the ball causes it to accelerate in the direction of the force.
Acceleration is in the same direction as the force
The force is centripetal : it acts towards centre of the circle
3rd law:
Ball must pull on the central point of support with an equal and opposite force to the force pulling on the ball from the centre.
Force acting on the point of support acts outwards
Support of the ball:
Ball is supported because the rope is not horizontal
There is equilibrium/no resultant force in the vertical direction.
Weight of the ball is supported by the vertical component of tension.
Horizontal component of tension provides centripetal force
If a mass on the end of a string is whirled round in a horizontal circle until the string breaks, what is the subsequent path taken by the mass and explain why
A parabola in the vertical plane
This is because the centripetal force no longer acts.
Object continues to move tangent to the circle at that point because there is no forces acting in the HZN direction on the object so it continues in a straight line tangentially to the circle. (NEWTONS FIRST LAW)
Object will fall downwards as it is influenced by gravity.
Newtons First Law
Object in motion continues to move at the same velocity and in the same direction unless there is an external force acting on it.
