Circular motion

A-level Physics

Unit G484: The Newtonian World

Centripetal force & acceleration

A-level Physics

Unit G484: The Newtonian World

Centripetal force & acceleration

Circular motion

Learning objectivesAt the end of the lesson you will be able to:

Lesson focus• Centripetal acceleration and force

• use the equation for centripetal acceleration a = v2/r ;

• use the equation for centripetal force F = ma = mv2/r .

Circular motion

Learning outcomes

All of you should be able to

• recall the equation for centripetal acceleration;

• recall the equation for centripetal force;

• solve basic problems using these equations.

Most of you will be able to

• solve more complex problems using these equations.

Circular motion

x - arc lengthr - radius

θ - angle (in radians) subtended by arc length x

θr

x

u v

- u

v

Δv = v - uθ

θ ≈Δvv

i.e. Δv ≈ θv

θ =xr

(1)

(2)

LO 1: use the equation for centripetal acceleration

Deriving the equation for centripetal acceleration LOs

Circular motion

θr

x

u v

- u

v

Δv = v - uθ

θ =xr

(1)

Δv ≈ θv (2)

Combining (1) and (2) gives

Δv ≈ x vr

but x = vt Δv ≈ v2tr

i.e. Δvt

≈v2

r

i.e. a = v2

r

(as t and θ become

very small)

LO 1: use the equation for centripetal acceleration

Deriving the equation for centripetal acceleration LOs

Circular motion

θr

x

u v

- u

v

Δv = v - uθ

a = v2

r

since F = maF = mv2

r

LO 1: use the equation for centripetal acceleration

Deriving the equation for centripetal acceleration LOs