further mechanics

Question 1

Radians

Answer 1

In circular motion, it is more convenient to measure angular displacement in units of radians rather than units of degrees.

Question 2

conversion from degrees to radians

Answer 2

Question 3

Angular speed

Answer 3

The angular speed is the angle an object rotates through per second. Just as linear speed, v, is defined as distance / time, the angular speed, w, is defined as angle / time. The unit is rads-1 (radians per second).

Question 4

Answer 4

Question 5

Frequency and period in angular motion

Answer 5

Circular motion has a frequency and period. The frequency, f, is the number
of complete revolutions per second (revs-1 or hertz, Hz). The period, T, is the
time taken for a complete revolution (in seconds).

Question 6

centripetal acceleration

Answer 6

An object in uniform circular motion has a constant linear speed
However, it is continuously changing direction. Since velocity is the speed in a given direction, it, therefore, has a constantly changing velocity
The object therefore must be accelerating
This acceleration is called the centripetal acceleration and is perpendicular to the direction of the linear speed
Centripetal means it acts towards the centre of the circular path
The centripetal acceleration is caused by a centripetal force of constant magnitude that also acts perpendicular to the direction of motion (towards the centre)
This is a result of Newton’s Second Law
Therefore, the centripetal acceleration and force act in the same direction

Question 7

Centripetal Acceleration Formula

Answer 7

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 8

Derivation of formula for centripetal acceleration

Answer 8

Question 9

Centripetal Force

Answer 9

An object moving in a circle is not in equilibrium, it has a resultant force acting upon it
This is known as the centripetal force and is what keeps the object moving in a circle
The centripetal force (F) is defined as:
* 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 10

Examples of centripetal force

Answer 10

• The centripetal force is not a separate force of its own
• It can be any type of force, depending on the situation, which keeps an object moving in a circular path
• When solving circular motion problems involving one of these forces, the equation for centripetal force can be equated to the relevant force equation
• For example, for a mass orbiting a planet in a circular path, the centripetal force is provided by the gravitational force
• When an object travels in circular motion, there is no work done
• This is because there is no change in kinetic energy