Motion in a Circle

Question 1

Define the radian

Answer 1

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

Question 2

Define angular displacement + give an equation

Answer 2

the angle of arc through which the object has moved from its starting position
angular displacement (θ) = arc length / radius

Question 3

Angular displacement should be expressed in _______

Answer 3

radians

Question 4

Define angular speed + give an equation

Answer 4

the angular displacement per unit time
angular speed (ω) = angular displacement (Δθ) / time taken (Δt)

Question 5

Equation for angular speed of one revolution

Answer 5

angular speed (ω) = 2π / time period (T)

Question 6

Equation for speed (in the context of circular motion)

Answer 6

speed (v) = angular speed (ω) x radius (r)

Question 7

Explain the cause of centripetal acceleration

Answer 7

1. Newton’s first law states that an object remains at rest or travels at constant velocity unless it is acted on by a resultant force
2. In the case of an object moving at steady speed in a circle, we have a body whose velocity is not constant
3. Therefore, there must be a resultant force acting on the object
4. This force is known as the centripetal force, and is always directed towards the circle’s centre

Question 8

Define centripetal force

Answer 8

the resultant force on an object towards the centre of the circle when the object is rotating round that circle at constant speed

Question 9

Define centripetal acceleration

Answer 9

the acceleration of an object towards the centre of the circle when the object is rotating at constant speed round that circle

Question 10

Give 2 equations for centripetal acceleration

Answer 10

a = rω²
a = v²/r

Question 11

Derive 2 equations for centripetal force

Answer 11

F = ma
a = rω² or a = v²/r
Substitution gives:
F = mrω² and F = mv²/r

Question 12

Angles can be measured in _______. An angle of 2π rad is equivalent to ___°

Answer 12

radians, 360