An 8.0 m radius merry-go-roundcompletes one revolution every 7.0s. a. What is th

Question

An 8.0 m radius merry-go-roundcompletes one revolution every 7.0s.

a. What is the angular velocity of the merry-go-round?

b. With what speed ar children moving when they ride on the merry-go-round?

c. What is the centripetal acceleration these children feel when riding on the merry-go-round?

d. What is the average acceleration of each child over the course of half a revolution of the merry-go-round?

e. What is the average acceleration of each child ovet the course of a full revolution turn of the merry-go-round

Explanation / Answer

w = v/r : v=(2*pi*r)/t = 7.17m/s

(a) w = 7.17/8 = 0.897 rad/sec

(b) v=(2*pi*r)/t = 7.17m/s

(c) a= v^2/r = 6.42m/s^2

(d) it will be integral of 2*v^2/r *cos(k) along k where k varies from pi/2 to 0

OR for simplicity you can take it 2* v^2/r= 12.84m/s^2

(e) zero as during vector sum of all the acc it will acc. will cancel each other

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