Further Mechanics

Question 1

How many radians in 360 degrees?

Answer 1

2 pi

Question 2

Define angular velocity

Answer 2

Number of rotations per second

Question 3

Equation linking angular velocity and velocity

Answer 3

v = r * omega

Question 4

Equation linking centripetal acceleration and angular velocity?

Answer 4

a = r * omega^2

Question 5

The equation for centripetal force

Answer 5

F = mv^2/r

Question 6

Derive the formula for centripetal acceleration

Answer 6

* No vertical acceleration because at A and B the vertical components are the same

* Consider the horizontal components only

* a = Δv/Δt (1)

* v = - v sinΘ - v sin Θ (2)

* ω = α/t where α is the angle turned through

* Since v = ωr => v = αr/t

* Therefore v = 2Θr/t => t = 2Θr/v (3)

* Sub (2) and (3) into (1)

* a = -v^2 sin Θ / Θr

* When Θ is small sin Θ = Θ

* Θ is small as we are looking for instaneous accleration

* a = -v^2/r

* Since v = rω => a = -(rω)^2/r = - ω^2r

Question 7

Derive r = p/BQ

Answer 7

Force on a charged particle in a magnetic field F=BQv

Centripetal force F = mv^2/r

Equate

BQv = mv^2/r

r = mv/BQ

p = mv

r = p/BQ