If the angular velocity of a rotating object is doubled, what happens to its cen

If the angular velocity of a rotating object is doubled, what happens to its centripetal acceleration?

If the angular velocity of a rotating object is doubled, what happens to its centripetal acceleration?

Correct Answer: Centripetal acceleration becomes four times its original value.

Step 1: Understand what angular velocity (ω) is. It is how fast something is rotating.
Step 2: Know the formula for centripetal acceleration (a_c), which is a_c = ω²r, where r is the radius of the circular path.
Step 3: If the angular velocity (ω) is doubled, we write it as 2ω.
Step 4: Substitute 2ω into the centripetal acceleration formula: a_c = (2ω)²r.
Step 5: Calculate (2ω)², which is 4ω².
Step 6: Now, replace (2ω)² in the formula: a_c = 4ω²r.
Step 7: This shows that if the angular velocity is doubled, the centripetal acceleration becomes four times greater.

Centripetal Acceleration – Centripetal acceleration is the acceleration directed towards the center of a circular path, which is dependent on the square of the angular velocity and the radius of the circular path.
Angular Velocity – Angular velocity is the rate of change of angular position of a rotating object, typically measured in radians per second.
Relationship between Angular Velocity and Centripetal Acceleration – Centripetal acceleration increases with the square of the angular velocity, meaning if angular velocity is doubled, centripetal acceleration increases by a factor of four.