At the top of a vertical circular loop, the minimum speed for a body to maintain contact with the track is given by
Correct answer: A. v equals the square root of rg
- A. v equals the square root of rg
- B. v equals rg
- C. v equals zero
- D. v equals the square root of 2rg
Explanation
At the critical speed the normal reaction falls to zero and gravity alone provides the centripetal force, so mg equals mv squared over r and v is the square root of rg. Any slower and the body leaves the track before reaching the top. This is the calculation behind loop the loop rides and the bucket of water swung overhead.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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