motion in a circle

Question 1

angular displacement

Answer 1

θ= ˢ⁄ᵣ

s is the arc length
r is the radius
θ is the angle in the circle

Question 2

angular velocity

Answer 2

rate of change of angular displacement

ω= θ⁄t

Question 3

why does an object travelling in a circle with constant speed have an acceleration

Answer 3

the object travelling in a circle has a velocity that is constantly changing, even though its speed is constant. hence, it has an acceleration that acts towards the centre of the circle.

Question 4

for a particle moving in a horizontal circle with constant angular velocity, is there any change to its linear momentum and kinetic energy?

Answer 4

the linear momentum is changing since the direction of the velocity is changing

since the angular velocity is constant, the speed of the particle is constant -> KE is constant

Question 5

relationship between angular and linear velocity

Answer 5

v = r ω

v is linear velocity
r is radius
ω is angular velocity

Question 6

angular velocity for one complete revolution

Answer 6

ω= θ⁄t = 2π⁄ T = 2πf

where T= ¹⁄f

Question 7

why does the object need to experience an acceleration?

Answer 7

although the magnitude of the velocity is constant, it’s velocity is changing as the direction of its motion is always changing. in order to change the velocity, this acceleration is required.

Question 8

direction of the acceleration to cause a change in velocity w/o change in magnitude?

Answer 8

towards centre of the circle

Question 9

centripetal acceleration

Answer 9

a = v²⁄r OR rω²

Question 10

centripetal force

Answer 10

• needs to be provided by an external force
• magnitude of the force that is required to keep the object moving in a circular path

F = ma = mv²⁄r OR mrω²

Question 11

centripetal force vs external force

Answer 11

Fext > Fc :
object will spiral towards centre of circular motion

Fext = Fc :
object will move in a circular motion

Fext < Fc :
object will spiral away from the centre of circular motion

Question 12

if friction provides centripetal force for a car to move in circular path, what is the WD by the frictional force?

Answer 12

there is no WD by the frictional force

throughout the motion, the direction of the frictional force is always perpendicular to the direction of displacement -> WD=0

Question 13

tension in string

Answer 13

highest point: minimum tension

lowest point: maximum tension (most likely to break)