What happens to the centripetal acceleration of a revolving body if you double the orbital speed v and halve the angular velocity omega?
Answers
Answer:
Centripetal acceleration will remain unchanged.
Explanation:
We need to find that,
what change will occur in the centripetal acceleration of a revolving body, if we double the orbital speed 'v' and halve the angular velocity 'ω'
The formula for angular acceleration is given by,
→ a = v²/r
and,
The formula for angular velocity is given by,
→ ω = v/r
[ where 'a' is centripetal acceleration, 'v' is the linear velocity of the body and 'r' is the radius and 'ω' is the angular velocity of the body ]
So, using both the formulae
→ a = v²/r
→ a = v²/(v/ω) [∵ r = v/ω]
→ a = v²ω/v
→ a = v ω
So, we now got the relation between angular acceleration, linear velocity and angular velocity.
It is given that, orbital speed is doubled and angular velocity is halved, therefore,
new angular velocity = ω/2
new linear (orbital) velocity = 2v
So,
→ new acceleration, a' = (2v) (ω/2)
→ a' = v ω
That means new angular acceleration is equal to the initial angular acceleration of the body.
Ultimately,
On doubling the orbital speed and halving the angular velocity of the body NO CHANGE will occur in the angular acceleration of the revolving body.
Answer:
.
The new centripetal
acceleration is same as the
initial acceleration.
.
