Chapter 17 - Motion in a circle

Question 1

What is one radian?

Answer 1

The angle subtended by a circular arc with a length equal to the radius of the circle.

Question 2

What is the equation for arc length?

Answer 2

l = rθ

Question 3

What is the angle of a whole circle?

Answer 3

360°

2π

Question 4

How do you convert from degrees to radians?

Answer 4

Angle in degrees x π/180

e.g. 50° = 50 x π/180 =

Question 5

What is circular motion?

Answer 5

The movement of an object along the circumference of a circle.

Question 6

What is angular displacement?

Answer 6

The vector measurement of the angle through which something has moved.

θ = l/r

Question 7

What is the equation for angular velocity involving angular displacement?

Answer 7

ω = θ/t
ω = 2π/T = 2πf

Question 8

What is the period of circular motion?

Answer 8

The time taken for one complete revolution.

Question 9

The instantaneous velocity is always ___________ to the radius of the circular path of an object.

Answer 9

The instantaneous velocity is always perpendicular to the radius of the circular path of an object.

Question 10

An object in circular motion is accelerating due to _______ __________ _______. This acceleration is always acting towards the ______ __ ____ ________ _____.

Answer 10

An object in circular motion is accelerating due to changing instantaneous velocity. This acceleration is always acting towards the centre of the circular path.

Question 11

What is the centripetal force?

Answer 11

The resultant force acting towards the centre of the circle that keeps an object moving at a constant speed along a circular path.
The force that causes the centripetal acceleration.

Question 12

What is the centripetal force acting on a car on a hill?

Answer 12

The resultant force of the weight of the car and the normal contact force (R) of the hill.
      2
 mv
------   = mg - R
  r

Question 13

What must happen for a car to lose contact with a hill?

What is the equation for speed required to do this?

Answer 13

The normal contact force of the hill must equal 0.
                     2
                mv
R = mg - ------- = 0
                  r
  2
v   = gr

Question 14

What is the centripetal force acting on a car around a roundabout?

Answer 14

The sideways friction between the car’s tyres and the road surface acting towards the centre of the roundabout.

Question 15

What must be the case for no skidding or slipping to occur on a roundabout?

Answer 15

The force of friction must be less than the limiting force of friction (maximum value of friction (determined by weight of car)).

Question 16

What causes the centripetal force of a vehicle on a banked track?

Answer 16

The sum of the horizontal components of the normal contact force on each wheel of the vehicle.
                               2
                          mv
(N1 + N2)sinθ = -----
                            r

Question 17

What is the equation for the condition for no sideways friction acting on a moving object on a slope?

Answer 17

2

v = grtanθ