If the speed of an object in circular motion is doubled, what happens to the centripetal acceleration?
Practice Questions
1 question
Q1
If the speed of an object in circular motion is doubled, what happens to the centripetal acceleration?
It remains the same
It doubles
It quadruples
It halves
Centripetal acceleration a_c = v²/r. If v is doubled, a_c increases by a factor of 4.
Questions & Step-by-step Solutions
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Q
Q: If the speed of an object in circular motion is doubled, what happens to the centripetal acceleration?
Solution: Centripetal acceleration a_c = v²/r. If v is doubled, a_c increases by a factor of 4.
Steps: 7
Step 1: Understand the formula for centripetal acceleration, which is a_c = v²/r, where 'a_c' is centripetal acceleration, 'v' is the speed of the object, and 'r' is the radius of the circular path.
Step 2: Identify what happens when the speed 'v' is doubled. If the original speed is 'v', the new speed will be '2v'.
Step 3: Substitute the new speed into the formula. The new centripetal acceleration will be a_c = (2v)²/r.
Step 4: Calculate (2v)². This equals 4v².
Step 5: Substitute 4v² back into the centripetal acceleration formula: a_c = 4v²/r.
Step 6: Compare the new centripetal acceleration (4v²/r) to the original centripetal acceleration (v²/r). Notice that the new acceleration is 4 times the original acceleration.
Step 7: Conclude that if the speed of an object in circular motion is doubled, the centripetal acceleration increases by a factor of 4.
