Mr. Kovall's Neighborhood

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Go to Circular Motion Notes

Go to Answers to Problems  (revised 02-03-06)

Part 2:  Circular Motion Problems –

Banked Turns and Orbital Dynamics

 

  1. At what angle should a curve of radius 150 m be banked so cars can safely travel at 25 m/sec without relying on friction?  Go to Solution.

 

  1. A curve of radius 120 m is banked at an angle of 18 degrees.  At what speed can it be negotiated under icy conditions where friction is negligible?

 

  1. A jet (mass = 2.00 x 105 kg), flying at 123 m/sec, banks to make a horizontal circular turn.  The radius of the turn is 3810 m.  Calculate the necessary lifting force.  Go to solution.

 

  1. A satellite is placed in orbit 6.00 x 105 m above the surface of Jupiter.  Jupiter has a mass of 1.9 x 1027 kg and a radius of 7.14 x 107 m.  Find the orbital speed of the satellite.  After solving this problem, go to: Jovian orbit.

 

  1. A satellite is in a circular orbit around an unknown planet.  The satellite has a speed of 1.70 x 104 m/sec, and the radius of the orbit is 5.25 x 106 m.  A second satellite also has a circular orbit around this same planet.  The orbit of this second satellite has a radius of 8.60 x 106 m.  What is the orbital speed of the second satellite?

 

  1. The surface of a cylindrical space station is rotating at 35.8 m/sec.  What must be the value of its radius for the astronauts quartered within to weigh one-half of their Earth weight?

 

  1. Michael works for Rainbow Rockets, Inc., and is about to transmit data to a space probe about to orbit Venus.  Venus rotates slowly about its axis, the period being 243 days.  The mass of Venus is 4.87 x 1024 kg.  What radius has Michael determined for a synchronous satellite orbit about Venus?  After solving this problem, go to: Venusian orbit.

 

  1. A spy satellite is about to be inserted into Terran orbit by “Magenta”, the alias of a certain member of our class who works for RBO (Rainbow Black Ops.).  The 907.44 kg satellite is expected to operate 600 km above the earth’s surface. Determine the speed necessary to maintain this orbit.

 

  1. Two satellites, A and B, are in different circular orbits about Earth. The orbital speed of satellite A is twice that of satellite B.  Find the ratio (TA/TB) of the periods of the satellites.

 

  1. A pilot of a 7.45 x 103 kg stealth bomber maintains a constant velocity as he continues a banked turn of 805 m from his target.  He experiences 3 g’s throughout the turn.  Determine the following variables:
    1. The tangential speed of his plane.
    2. The force the bomber’s seat exerts against his body.
    3. The lift provided by the air beneath his plane.
    4. The angle his plane must maintain relative to the vertical.  Go to solution.

 

  1. The coefficient of static friction between the tires of a motorcycle and the road is µS = 0.56.  At a speed of 19 m/sec, what is the radius of the tightest unbanked turn that the driver can hope to handle?
  2. A boy is riding a merry-go-round at a distance of 7.00 m from its center.  The boy experiences a centripetal acceleration of 7.50 m/sec2.  What centripetal acceleration is experienced by another person who is riding at a distance of 3.00 m from the center?

 

  1. A helicopter rotor turns at a rate of 315 rpm.  The tip of one of the blades moves in a circle whose radius is 7.50 m.
    1. What is the speed of the tip of the blade?
    2. What is the centripetal acceleration of the tip of the blade?  (express your answer in multiples of g = 9.80 m/sec2)

 

  1. A ceiling fan has two different angular speed settings: f1 = 440 rev/min and f2 = 110 rev/min.  What is the ratio a1/a2 of the centripetal accelerations of a given point on one of the fan blades.   

    Go to Solutions to #13 and 14

 

  1. A basketball player is balancing a spinning basketball on the tip of his finger.  The angular velocity of the ball slows down from 19.0 to 16.2 rad/sec, during which the angular displacement of the ball is 79.2 rad.  Determine the time it takes for the ball to slow down.

 

  1. A turntable is switched from 45 rpm to 33.33 rpm, and the platter rotates through an angle of 11.5 rad in reaching the new angular speed.  What is the angular acceleration of the platter?

    Go to Solutions to #15 and 16

 

  1. The drill bit of a variable-speed electric drill has a constant angular acceleration of 2.50 rad/sec2.  The initial angular speed of the bit is 5.00 rad/sec.  After 4.00 sec,
    1. What angle has the bit turned through?
    2. What is the bit’s angular speed?

 

  1. An airliner arrives at the terminal, and the pilot shuts off the engines.  The initial angular velocity of the fan blades is 1800 rad/sec, and it takes 120 sec for them to come to rest. What is the angular displacement of the blades?

 

  1. A wheel accelerates so that its angular speed increases from 150 to 580 rad/sec in 16 revolutions.  What is the angular acceleration in rad/sec?

 

  1. Determine the equivalent in radians for the following: 45º, 180º, and 360º.

  21.  A spherical space station is constructed while in orbit and has a diameter of 24 km.

            a.   At what velocity must it revolve if an astronaut walking on its inner surface is to experience a weight that is three times greater than his weight on Earth?

            b.   What is the station's angular velocity?

            c.   What is the station's period of rotation?