Circular motion

Question 1

Define an angle in radians

Answer 1

its defined as the arc length divided by the radius of the circle

Question 2

What is the arc length for a complete circle (360º) ?

Answer 2

the arc length is simply the circumference of the circle , 2π

Question 3

Define angular velocity , ω.

Answer 3

its the angle an object rotates through per second

Question 4

State the equation for angular velocity

Answer 4

ω = θ / t

ω- angular velocity ( rad s¯¹)

θ - angle ( radians )

t- time (s)

*angular velocity is a vector quantity as it has both magnitude and a direction

Question 5

What is meant by the frequency of an object in circular motion?

Answer 5

the number of complete revolutions per second (rev s¯¹ , hertz or Hz )

Question 6

What is meant by the period of an object in circular motion?

Answer 6

the time taken for a complete revolution to occur

Question 7

What causes an object to travel in a circular path?

Answer 7

an object will travel in a circular path if there is a constant net force acting on it perpendicular to its velocity (a.k.a a centripetal force)

Question 8

How do you convert degrees to radians

Answer 8

multiply angle by π and divide by 180

Question 9

What kind of force causes an object to travel in a circular path?

Answer 9

a constant net force perpendicular to the velocity of the object (centripetal force - it always acts towards the centre of the circle)

Question 10

How are linear and angular velocity related?

Answer 10

v = ⍵r

Where v = linear velocity (ms¯¹) , ⍵ = angular velocity (rad s¯¹) , and r = radius (m)

Question 11

An object moving in a circle at a constant speed is not accelerating. True or False?

Answer 11

False.

The direction is always changing hence the velocity is always changing which means it is accelerating

Question 12

State acceleration in terms of angular and linear velocity

Answer 12

a=⍵²r

a = v²/r

Question 13

What are the equations for centripetal force?

Answer 13

F = mv²/r

or

F = m⍵²r

Question 14

Describe the steps as to how one can investigate circular motion via an experiment

Answer 14

Equipment: bung , piece of string , glass tube and masses

1. Measure mass of bung then tie it to the piece of string.Thread string through glass tube ,and weigh down free end using mass/washers (these provide centripetal force as tension throughout string is constant)
2. make reference mark on string , then measure distance from mark to centre of bung
3. Line mark up with top of glass tube then begin to spin bung in horizontal circle (try to keep reference level in line with top of glass tube )
4. Measure time taken for bung to make 10 complete circles then divide to get average
5. Use 2π/t to find angular velocity and F= mb⍵²r to get centripetal force
6. centripetal force should equal weight of mass/washers (Mg=m²⍵/r)