Circular Motion

Question 1

Why is an object in uniform circular motion with a constant linear speed always accelerating

Answer 1

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

Question 2

What is the acceleration of an object in uniform circular motion called and in what direction does it act

Answer 2

It is called centripetal acceleration
It is perpendicular to the direction of the linear speed and always acts towards the centre of the circle

Question 3

What is the direction of velocity

Answer 3

At a tangent to the circle

Question 4

What direction is the centripetal force in

Answer 4

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

Question 5

What is centripetal acceleration caused by

Answer 5

A centripetal force of constant magnitude that also acts perpendicular to the direction of motion (towards the centre)

Question 6

Angular displacement of a body in circular motion

Answer 6

The change in angle, in radians, of a body as it rotates around a circle

Question 7

What is angular displacement the ratio of

Answer 7

Distance travelled around the circle : Radius of the circle

Question 8

Radian

Answer 8

The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle

Question 9

Equation for angular displacement (theta) in relation to the arc length and radius of the circle

Answer 9

theta = arc length / radius

Question 10

Angular velocity (w) of a body in circular motion

Answer 10

The rate of change in angular displacement with respect to time

Question 11

Units for angular velocity

Answer 11

rad / s

Question 12

Equation linking angular velocity, time and theta

Answer 12

angular velocity = theta / Time

Question 13

Equation linking angular velocity, linear velocity and radius of the circle

Answer 13

angular velocity = linear velocity / radius

Question 14

Equation linking angular velocity, 2pi and frequency / time period

Answer 14

angular velocity = 2pi x frequency
OR
angular velocity = 2pi / Time period

Question 15

Centripetal acceleration

Answer 15

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

Question 16

Equation linking acceleration, linear speed and radius

Answer 16

centripetal acceleration = linear speed ^2 / radius

Question 17

Why is an object moving in a circle not in equilibrium

Answer 17

It has a resultant force acting on it - the centripetal force.
This force keeps the object moving in a circle

Question 18

Centripetal force

Answer 18

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

Question 19

What is the centripetal force for a car travelling around a roundabout

Answer 19

Friction between car tyres and the road

Question 20

What is the centripetal force for a ball attached to a rope and moving in a circle

Answer 20

Tension in the rope

Question 21

What is the centripetal force for the Earth orbiting the Sun

Answer 21

Gravitational force

Question 22

Why is the kinetic energy of a particle moving in a circle with uniform speed constant

Answer 22

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.

Question 23

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

Answer 23

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

Question 24

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

Answer 24

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.

Question 25

Newtons First Law

Answer 25

Object in motion continues to move at the same velocity and in the same direction unless there is an external force acting on it.