Question

Is this formula regular?

"Is linear velocity found like this: the square root of centripetal acceleration over the radius?"
A. Yes, it's a valid formula for linear velocity.
B. No, it's not a valid formula for linear velocity.
C. It depends on the specific situation.
D. Linear velocity is unrelated to centripetal acceleration.

Answer 1

The stated formula for finding linear velocity is incorrect. The correct relationship for linear velocity in circular motion is v = √(ac × r), where ac is centripetal acceleration and r is the radius of the circular path.

Step-by-step explanation:

The formula mentioned in the question, linear velocity = √(centripetal acceleration/radius), is not the correct expression for calculating linear velocity. Instead, the correct relationship between centripetal acceleration (ac) and linear velocity (v) in circular motion is given by the equation ac = v²/r, where ac is the centripetal acceleration, v is the linear velocity, and r is the radius of the circular path. When solving for v, it leads to the formula v = √(ac × r).

The centripetal acceleration is always directed towards the centre of the circle and is a result of a change in the direction of the velocity, not its magnitude. Whereas the linear velocity(also referred to as tangential speed) involves a change in position over time along the circular path. The linear velocity is related to the angular velocity (w) by the equation v = rw, where w is the angular velocity in rad/s.

Therefore, the answer to whether the formula is regular for calculating linear velocity is B. No, it's not a valid formula for linear velocity.