Suppose you swing a ball on a verical circle on 0.800 m-longstring. As you know

Question

Suppose you swing a ball on a verical circle on 0.800 m-longstring. As you know from experience there is a minimumangular velocity min you must maintain if you wantthe ball to complete the full circle. If you swing the ballat <min, then the string goes slackbefore the ball reaches the top of the circle. What is min in rpm? Suppose you swing a ball on a verical circle on 0.800 m-longstring. As you know from experience there is a minimumangular velocity min you must maintain if you wantthe ball to complete the full circle. If you swing the ballat <min, then the string goes slackbefore the ball reaches the top of the circle. What is min in rpm?

Explanation / Answer

I had the same question but with diff numbers.Here is how u solve it. Suppose you swing a ball in a vertical circleon a 0.700 m-long string. As you probably know from experience,there is a minimum angular velocity you must maintain if you wantthe ball to complete the full circle. If you swing the ball atw<w_min, then the string goes slack before the ball reaches thetop of the circle.

• w should be such that at the top T > 0 Thatis possible only if mw^r, the centripetal force required is greaterthan mg or
  w^2 r > g or w^2 > g/r or w > sq rt(g/r) = sq rt(9.8/7) =sq rt(1.4) = 1.18
  So w_min = 1.18 rad/s = 1.38/2pi = 1.18/(2x3.14) = 0.188 rev/s or =11.3 rpm

• w should be such that at the top T > 0 Thatis possible only if mw^r, the centripetal force required is greaterthan mg or
  w^2 r > g or w^2 > g/r or w > sq rt(g/r) = sq rt(9.8/7) =sq rt(1.4) = 1.18
  So w_min = 1.18 rad/s = 1.38/2pi = 1.18/(2x3.14) = 0.188 rev/s or =11.3 rpm

w should be such that at the top T > 0 Thatis possible only if mw^r, the centripetal force required is greaterthan mg or
w^2 r > g or w^2 > g/r or w > sq rt(g/r) = sq rt(9.8/7) =sq rt(1.4) = 1.18
So w_min = 1.18 rad/s = 1.38/2pi = 1.18/(2x3.14) = 0.188 rev/s or =11.3 rpm w should be such that at the top T > 0 Thatis possible only if mw^r, the centripetal force required is greaterthan mg or
w^2 r > g or w^2 > g/r or w > sq rt(g/r) = sq rt(9.8/7) =sq rt(1.4) = 1.18
So w_min = 1.18 rad/s = 1.38/2pi = 1.18/(2x3.14) = 0.188 rev/s or =11.3 rpm w should be such that at the top T > 0 Thatis possible only if mw^r, the centripetal force required is greaterthan mg or
w^2 r > g or w^2 > g/r or w > sq rt(g/r) = sq rt(9.8/7) =sq rt(1.4) = 1.18
So w_min = 1.18 rad/s = 1.38/2pi = 1.18/(2x3.14) = 0.188 rev/s or =11.3 rpm

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