Mr. Kovall's Neighborhood

Return to Honors Physics Home Page

Go to Solutions to Circular Motion Problems: (doc.) (htm.)

Go to Circular Motion Notes  Go to Formula Sheet   (Revised 02-03-06)

Part1:  Circular Motion Problems

  1. A fly is sunning itself on a phonograph record at a point 15 cm from the center.  The record is rotating at 78 rev/min and the fly has a mass of 5 grams.
    1. What is the linear velocity of the fly?
    2. What is the angular velocity of the fly?
    3. What is the centripital acceleration of the fly?
    4. What is the angular acceleration of the fly?
    5. What force will the fly experience?

 

  1. The hour hand of a clock is 18 cm long, from the center of the dial to the tip of the hand.  Determine the following quantities a lightning bug will experience, if it lands on the tip of the hour hand:
    1. It’s linear velocity.
    2. It’s angular velocity.
    3. It’s centripital acceleration.
    4. It’s angular acceleration.

 

  1. A satellite whose diameter is 15 km is located 1.9 x 105 km from Earth (ME = 5.98 x 1024 kg) and is in a nearly circular orbit.  Go to Solution
    1. What is the linear velocity of the satellite?
    2. What is the angular velocity of the satellite?
    3. What is the satellite's centripital acceleration?
    4. What is the satellite's period?
    5. What "g" does the satellite experience?

 

  1. A spaceman within the satellite in problem #3 experiences a local field equal to that of Earth.
    1. What must be the satellite’s angular velocity?
    2. What must be the satellite’s angular velocity if the local field within is 3 g’s?
    3. What is the period of rotation for both local fields?
    4. What is the rate of rotation for both local fields?

     

  1. A 90 ft diameter ferris wheel at Disney World is rotating at 6 rpm.  Calculate:
    1. The force acting on a 175-lb man riding in one of the cars.
    2. The force acting on the man’s 125-lb daughter?

 

  1. A 180-lb pilot is flying at 540 mi/hr when he enters the pull out phase of a power dive.  What is the smallest radius curve that he will be able to use if his centripetal acceleration cannot exceed 7 g’s without blacking out?

 

  1. The minute hand of a wristwatch is 1.3 cm long from the center of the dial to the tip of the hand.  Calculate:
    1. The linear and angular velocity of the hand.
    2. The acceleration of the hand.

 

  1. An aviator makes a 120 m radius loop and cannot exceed an acceleration of 4 g’s.  Calculate his minimum:
    1. Linear velocity.
    2. Angular velocity.

 

  1. A 2 m length of rope is capable of supporting a maximum weight of 150 Nt without breaking.  This rope is then whirled in a circle with a 3 kg object attached.  Calculate the object’s:
    1. Linear velocity.
    2. Angular velocity.
    3. Period of rotation

 

  1. A 2-gram fly is sunning itself on a phonograph record 4 cm from the center.  The turntable is turned on at 45 rpm.
    1. What is the fly’s linear velocity?
    2. What is the fly’s angular velocity?
    3. What is the fly’s acceleration?
    4. If the turntable is changed to 33 1/3 rpm, how much greater or less would your answers be for parts a, b, and c.

 

  1. An 80 ft ferris wheel is rotating at 8 rpm.  Calculate its:
    1. Linear velocity
    2. Angular velocity
    3. Acceleration

 

  1. Determine the following for a pilot in a plane performing a power dive with a velocity of 360 mi/hr, if his local field may not exceed 3.5 g’s:
    1. His path’s smallest radius curve.
    2. His angular velocity.

 

  1. The second hand on a clock is 15 cm long from the center of the dial to the tip of the hand.  Calculate the tip of the hand’s:
    1. Angular velocity
    2. Linear velocity
    3. Acceleration

 

  1. A piece of cable can just support 620 Nt without breaking.
    1. What is the maximum angular velocity with which a 5 kg mass, attached to this cable, may be rotated in a 50 cm radius circle without breaking the cable?
    2. What is its linear velocity?
    3. What is its rate of rotation?
  1. Determine the following for a plane:
    1. The smallest possible radius curve in which the plane may turn if it is traveling at 195 ft/sec and the largest force that the pilot is able to withstand without blacking out is 4 g’s?
    2. What would be his angular velocity in this turn?

 

  1. The tip of the hour hand of a clock is 1.5 cm from the center of the dial.  Calculate the tip’s:
    1. Linear velocity.
    2. Angular velocity.
    3. Linear acceleration.
    4. Angular acceleration.

 

  1. A pilot makes a 150 m radius loop and is physically unable to be exposed to a force of 7 g’s.  Calculate his:
    1. Maximum linear velocity.
    2. Maximum angular velocity.
    3. Minimum time required to complete one loop.

 

  1. A 0.6 g fly is sunning itself on a circular rotating table that is turning at 20 rpm and it experiences a force of 3 dynes.  Find the fly’s:
    1. Linear velocity.
    2. Angular velocity.
    3. Distance from the center of rotation.
    4. Linear acceleration.
    5. angular acceleration.

 

  1. You are listening to your favorite 33 1/3 rpm record on the stereo.  The record has a scratch on the surfaced 5 cm from the center of the record.  Calculate the scratch’s:
    1. Linear velocity.
    2. Angular velocity.

 

  1. A 5-lb weight is whirled in a circle at the end of an 8 ft wire.  The weight is rotating at 90 rpm.  What is the weight’s:
    1. Angular velocity
    2. Linear acceleration
    3. Angular acceleration
    4. Centripetal force
    5. Angle through which the weigh turns in 5 seconds.

 

  1. A 2 kg object is on the end of a 250 cm wire that is whirled in a circle at 120 rpm.  What is the object’s:
    1. Linear velocity
    2. Angular velocity
    3. Centripetal force (neglect gravity)

 

  1. A 60 ft diameter merry-go-round rotates at 5 rpm.
    1. What is the edge’s angular velocity?
    2. What is the edge’s linear velocity?
    3. What is the edge’s centripetal acceleration?
    4. What is the centripetal force acting on a 160-lb man standing on the outer edge?
    5. What is the man’s angular acceleration if the merry-go-round comes to rest in 2 minutes?
 23.  A 4.5 x 103 kg rocket ship is traveling through space at 230 m/sec. A rocket that exerts a force of 1300 Nt is fired off at one side in such  a way as to change the ship’s direction of travel.  The ship turns as necessary to keep its nose pointed in the direction in which it is traveling.
    1. What is the radius of the circular orbit of the rocket ship?
    2. What is the ship’s angular velocity?
    3. What is the ship’s period of rotation?

 

  24.   A 70-lb boy sits 12 ft from the center of rotation on a spinning platform in an amusement park.  The platform is spinning at 4.5 rpm.
    1. What is the boy’s linear velocity?
    2. What is the boy’s angular velocity?
    3. What is the boy’s acceleration?
    4. What is the boy’s period of revolution?

 

  25.   Calculate the angular acceleration of a 25 ft radius wheel which starts from rest and achieves a velocity of 475 ft/sec in one minute.
    1. What is its angular velocity after one minute?
    2. What is its final acceleration after one minute?

 

 26.  If a wheel that is 45 cm in radius turns with a velocity of 750 rads/sec,

            a.   what is its centripetal acceleration?

            b.   how much greater would its rate of revolution be if its radius were to be doubled?

            c.   what would happen to its linear velocity with the new radius?

            d.   what would happen to its linear acceleration?

 

 27.  A ball of mass 1.5 x 102 kg is swung in a horizontal circle at the end of a 4.8 m length of string.  If the ball is to rotate at 4.6 m/sec,

            a.   what force does the ball exert on the string?

            b.   what is the ball's angular velocity?

            c.   what is the ball's rate of revolution?

 

 28.   A wheel 18 inches wide starts from rest and achieves a velocity of 475 ft/sec in three minutes.

            a.   Calculate its angular acceleration.

            b.   What is the wheel's angular velocity after two minutes?

            c.   What is its final linear acceleration after three minutes of elapsed time?

 

 29.   The rate of revolution of a 16-inch diameter sanding disc is changed from 78 rpm to 45 rpm.  If it takes 0.4 seconds for the speed change to take place,    Go to Solution

            a.   what is the angular acceleration experienced by a 0.45 ounce wood fiber on the outer edge of the disc?

            b.   what is the change in the angular velocity of a point 5-inches from the outer edge of the disc?

            c.   what is the change in centripetal force acting on the fiber of wood?

 

30. Calculate the centripetal force needed to keep a 30 Nt body moving in a circle with a diameter of 2000 cm at a speed of 12 m/sec.

 

 

 

Self-Test Problems

  1. A body in uniform circular motion has:
    1. Zero acceleration.
    2. Acceleration that is constant in direction, but not in magnitude.
    3. Acceleration that is constant in magnitude, but not in direction.
    4. Linear acceleration.
  1. Which of the following is true of an object moving in a circle at a constant speed?
    1. The object has a velocity along a radius.
    2. The object has a changing velocity.
    3. The object has an acceleration along a tangent.
    4. The rectilinear displacement of the object is constant.
  1. Angular velocity is directly proportional to:
    1. Time
    2. Mass
    3. Rate of revolution
    4. Circumference
  1. If the time for one revolution is doubled, then the acceleration will be:
    1. Doubled
    2. Quartered
    3. Quadrupled
    4. None of the above
  1. If the force applied to a given 1 kg mass is halved, the angular velocity will be approximately:
    1. Quartered
    2. Doubled
    3. 1.4 times greater
    4. 2.5 times greater
    5. 0.71 times the original
  1. Which of the following is not being accelerated:
    1. A freely falling stone.
    2. A satellite in a stable circular orbit.
    3. A car moving with a constant velocity.
    4. A bullet in its trajectory.