VDU_Physics_1_006

Physics 1.-  Mechanics:   Circular Motion

Javier Montenegro Joo

jmj@VirtualDynamics.Org

Circular motion.-

(1) A 10-cm diameter frictionless disk is rotating about its axis at 1000 rpm.  Suddenly while the disk is rotating, a particle located at a distance of half radius gets released and it is triggered. Determine the shooting speed of this particle.

Solution.-

The angular speed of the disk is the same at any radial distance, hence the initial velocity of the released particle is:

[01234]

(2) A 120 gr ball is tied to the end of a string of 3 m which is rotating with its other end fixed to a rotating shaft. The ball describes a circular orbit and moves with an acceleration of 10 m/s2 .  When the acceleration vector makes an angle of 25o  with rope, calculate (a) radial acceleration (b) tangential acceleration (c) speed of the ball.

Solution.-

(5) Two wheels whose diameters are 40 cm and 60 cm, respectively, are on the same plane and they are separated. Both wheels are connected by a belt passing around their edges. Determine the angular velocity of the larger wheel when the smaller wheel rotates at 600 rpm. Calculate the distance traveled during 7.5 min by a point of the belt.

Solution.-

The tangential velocity of both wheels is the same, then:

[56789]

Accelerated Circular Motion.-

(3) A disk of 2.5 kg and 1 m diameter is rotating at 3000 rpm when it is disconnected from the source of energy that keeps it rotating. For the moment just before disconnection calculate: (a) angular speed of the disc (b) tangential speed of a point on the edge of the disc, (c) centripetal acceleration of a point on the edge of the disc (d) If the disk stops 30 s after disconnection, determine how many turns are completed during that time.

Solution.-

(4) A 2.50 m diameter disk starts rotating with an angular speed of 1.75 rad/s and a constant acceleration of 1.60 rad/s2 .  For a dot at the edge of the disk and for 1.50s after initiated the motion, calculate: (a) Displacement, (b) Angular velocity, (c) Tangential velocity, (d) Magnitude of the acceleration vector, (e) Angle between acceleration and radius.

Solution.-