circular motion

Question 1

what is the formula for angular displacement?

Answer 1

θ=s/r
s = arc length
r = radius

Question 2

is angular displacement a vector or a scalar?

Answer 2

vector (CW/ACW)

Question 3

how to convert degrees to radians?

Answer 3

1 deg x π/180 = 0.01745 rad

Question 4

what is the definition of angular velocity?

Answer 4

angular velocity, ω, of an object is the rate of change of angular displacement with respect to time

Question 5

is angular velocity a scalar or a vector?

Answer 5

vector (CW/ACW)

Question 6

what is the formula for angular velocity and what is its unit?

Answer 6

ω=θ/t
rad sˆ-1

Question 7

in radians, how long is one revolution?

Answer 7

2π radians

Question 8

what is the formula relating period?

Answer 8

T=2π/ω

Question 9

what is the formula relating angular velocity to linear velocity?

Answer 9

v=rω

Question 10

convert 300rpm to angular velocity

Answer 10

300rpm = 5rps = 5 x 2π sˆ-1 = 10π sˆ-1
= 31.4 rad sˆ-1

Question 11

when does a force cause only the direction of velocity to change?

Answer 11

when the force acts perpendicular to velocity

Question 12

in uniform circular motion, why is there an acceleration towards the centre of the circle?

Answer 12

• velocity is a vector with both direction and magnitude
• a mass moving in such motion is always changing in velocity due to change in direction
• thus the mass will experience acceleration towards centre of circle, by N2L net force acts in same direction as acceleration

Question 13

why is there no work done by centripetal force?

Answer 13

• work done is force x displacement in the direction of the force
• since centripetal force is perpendicular to velocity, work done by centripetal force = 0
• thus no change in kinetic energy, speed remains constant

Question 14

what are the 2 formulas for centripetal acceleration?

Answer 14

a = vˆ2/r
a = rωˆ2

Question 15

what is the SOP to solving uniform circular motion questions?

Answer 15

1) FBD
2) draw direction of a (towards centre of circle)
3) apply N2L
F = ma, a =vˆ2/r or a = rωˆ@

Question 16

for non-uniform circular motion, what other concept is commonly applied?

Answer 16

conservation of energy

Question 17

what is the key understanding for minimum speed to stay in contact?

Answer 17

not to lose contact => N > 0
(N acts in same direction as W if object is on the loop-the-loop)

Question 18

what is lateral friction?

Answer 18

it acts towards the centre of the circle if the vehicle is moving in circular motion