Uniform Circular Motion (UCM) 4/25/07

Uniform Circular Motion UCM means that  is constant Which means that…

Uniform Circular Motion UCM means that  is constant Which means that… –  = 0

Uniform Circular Motion UCM means that  is constant Which means that… –  = 0 –a T = 0

Uniform Circular Motion UCM means that  is constant Which means that… –  = 0 –a T = 0 –|v T | = constant

Uniform Circular Motion UCM means that  is constant Which means that… –  = 0 –a T = 0 –|v T | = constant BUT… v T is not constant because the direction changes

Uniform Circular Motion If v T isn’t constant, this means there is an acceleration. In which direction is the acceleration? Hint: what is exerting the force on the ball?

Uniform Circular Motion If v T isn’t constant, this means there is an acceleration. If you let go of the string when the object is at the top of the arc, which way will the object go?

Centripetal Acceleration Centripetal = “Center-seeking” Equation a c = vT2vT2 r But v T = r  so a c = (r  ) 2 r = r  2 Units{a c } = ?

Centripetal Acceleration Centripetal = “Center-seeking” Equation a c = vT2vT2 r But v T = r  so a c = (r  ) 2 r = r  2 Units{a c } = m s2s2

Directions of Accelerations Acceleration Direction aT =aT = vTvT tt vTvT

Directions of Accelerations Acceleration Direction aT =aT = vTvT tt In line with v T vTvT aTaT

Directions of Accelerations Acceleration Direction aT =aT = vTvT tt In line with v T vTvT aTaT  = =  f -  o tt In line with 

Directions of Accelerations Acceleration Direction aT =aT = vTvT tt In line with v T vTvT aTaT  = =  f -  o tt In line with   

Directions of Accelerations Acceleration Direction aT =aT = vTvT tt In line with v T vTvT aTaT  = =  f -  o tt In line with    a c = vT2vT2 r = r  2 Towards center

Directions of Accelerations Acceleration Direction aT =aT = vTvT tt In line with v T vTvT aTaT  = =  f -  o tt In line with    a c = vT2vT2 r = r  2 Towards center

Centripetal Force F = ma

Centripetal Force F c = ma c = m vT2vT2 r or F c = ma c = mr  2

Centripetal Force The centripetal force is the net force on an object in circular motion vTvT

Centripetal Force The centripetal force is the net force on an object in circular motion vTvT

Centripetal Force The centripetal force is the net force on an object in circular motion vTvT

Example: A child on a merry-go-round is 2.5 m from the center. The child weighs 40 kg and the centripetal force on the child is 160 N towards the center. Find v T. 2.5 m