Central force
- (a) State the equation that relates radial acceleration and angular velocity.
(b) State the units of angular and radial acceleration.
(c) Explain the difference between angular and radial acceleration.
- Derive the expression a = rω2 for the radial acceleration of an object.
- The central force maintaining an object in a circular orbit is given by F = mrω2.
Sketch graphs showing the variations of:
(a) central force with mass of the object
(b) central force with radius of the object
(c) central force with angular velocity of the object.
- A piece of string has a breaking force of 56 N. This string is used to whirl a mass of 150 g in a horizontal circle.
(a) The 150 g mass moves in a horizontal circle of radius 1.2 m. Calculate the maximum angular velocity of the mass.
(b) The mass is rotated at 85 rpm. Find the maximum possible radius of the circular orbit.
- A swing ball, on a cord of length 1.5 m, has a mass of 2.0 kg. After being hit by a bat, the ball moves in a horizontal circle of radius 0.50 m with a steady speed of 1.33 m s-1.
(a) Draw a sketch showing the path of the ball on the string.
(b) Calculate the central acceleration of the ball.
(c) Draw a sketch showing all the forces on the ball while moving in a horizontal circle. Determine the tension in the string.
- A 3.0 kg mass is whirled in a vertical circle of radius 0.75 m at a steady speed of 8.0 m s-1.
(a) Calculate the tension in the string at the top of the circle.
(b) Calculate the tension in the string at the bottom of the circle.
- A hump backed bridge is in the form of a circular arc of radius 35 m.
What is the greatest speed with which a car can cross the bridge without leaving the ground at its highest point?
- (a) In a space flight simulator an astronaut is rotated at 20 rpm in a pod which is at the end of an arm of radius 5.0 m. Show that the central force on the astronaut is 2.2g.
(b) What rotation rate would give a ‘simulated’ gravity of 3g?
- Comment on the words centripetal and centrifugal with respect to angular motion.
