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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?
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Practice Questions
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Q1
If the angular velocity of a rotating object is doubled, what happens to its centripetal acceleration?
It remains the same
It doubles
It quadruples
It halves
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Centripetal acceleration (a_c) = ω²r. If ω is doubled, a_c becomes (2ω)²r = 4ω²r.
Questions & Step-by-step Solutions
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Q
Q: If the angular velocity of a rotating object is doubled, what happens to its centripetal acceleration?
Solution:
Centripetal acceleration (a_c) = ω²r. If ω is doubled, a_c becomes (2ω)²r = 4ω²r.
Steps: 7
Show Steps
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.
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