Question

What happens to the centripetal acceleration of
a revolving body if you double the orbital speed
v and halve the angular velocity ω ?
(a) the centripetal acceleration remains
unchanged
(b) the centripetal acceleration is halved
(c) the centripetal acceleration is doubled
(d) the centripetal acceleration is quadrupled.

Answer 1

Explanation:

Centripetal acceleration for uniform circular motion: a

c

=ω

2

r=ω

2

ω

v

t

=ωv

t

where ω is the angular velocity and v

t

is the tangential velocity.

∴a

c

′

=ω

′

v

t

′

Given ω

′

=

2

ω

; v

t

′

=2v

t

⇒a

c

′

=

2

ω

2v

t

ωv

t

=a

c