1a. An object is moving in a circular path of radius 4.00m. If the object moves

Question

1a. An object is moving in a circular path of radius 4.00m. If the object moves through a tangential distance of 3.00 meters. Calculate the angle the object travels through.

1b. A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 200 revolutions per minute, then what is the tangential velocity of a point on the circumference?

1c.A 4.0 kg mass is moving in a circular path of radius 2.5m with a constant tangential velocity of 5.0m/sec. What is the centripetal force on the mass?

Explanation / Answer

1a. Radius of the circlue is r = 4.00 m tangential distance d = 3.00 m Angular displacement is = d / r                                        = 3.00 m / 4.00m                                        = 0.75 rad ------------------------------------------------------------- 1b Radius of the disk is r = 12.0 cm / 2                                    = 6.00 cm                                    = 0.06 m   Angular velocity is = 200 rev/min                                  = (200 rev/min )( 2 rad/rev)(1 min /60s)                                                     = 20.93 rad/s Now the tangential velocity is v = r                                                 = 0.06 m * 20.93 rad/s                                                 = 1.256 m/s -------------------------------------------------------------- 1c Mass of the body is m = 4.0 kg radius is r = 2.5 m tangential velocity is v = 5.0 m/s Centripetal force is              F = mv2 / r                   = (4.0 kg)(5.0 m/s)2 / 2.5 m                 = 40.0 N

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