An object travels at constant speed v in a circle of radius r.How many times lar

Question

An object travels at constant speed v in a circle of radius r.How many times larger/smaller is the acceleration (a) if v isdoubled, (b) if r is doubled? What happens to a as r -> 0? Whycan't a car change direction instantaneously ( with not time delay)- how large would a have to be? A homework question i got wrong. I know a similar questionwill be on the exam and I want to know where and what part of thequestion I made my mistake. Please help. An object travels at constant speed v in a circle of radius r.How many times larger/smaller is the acceleration (a) if v isdoubled, (b) if r is doubled? What happens to a as r -> 0? Whycan't a car change direction instantaneously ( with not time delay)- how large would a have to be? A homework question i got wrong. I know a similar questionwill be on the exam and I want to know where and what part of thequestion I made my mistake. Please help.

Explanation / Answer

Accleration a = v^ 2 / r (a). from this a v ^ 2      ( a'/a ) = ( v'/ v ) ^ 2 Given v ' = 2v plug the values (a'/ a ) = ( 2v / v ) ^ 2                                   = 4                                a ' = 4 a i.e., accleration increases to 4 times (b). from above equation a 1/ r                                ( a' / a ) = ( r / r ' ) Given r ' = 2r plug the values ( a' / a ) = ( r / 2r )                                     = ( 1/ 2)                                  a' = a / 2 accleration decreases to half           

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