Rotational Kinematics

  1. Express the following angles in degrees, radians, and revolutions.

a)200

b)0.40 rad

c)1/3 rev

  1. Express the following angular speeds in degrees/second, radian/sec, rev/sec

a)0.020 rev/sec

b)300 /sec

c)1.4 rad/sec

  1. A wheel originally at rest is to reach an angular velocity of 36 rad/sec in 0.6 sec

a)What constant angular acceleration must it have?

b)What total angular displacement does it turn in 6 sec?

  1. A wheel turning with angular speed of 30 rev/sec is brought to rest with a constant acceleration. It turns 60 rev before it stops.

a)What is the angular acceleration in rad / sec2?

b)What time elapses before it stops?

  1. A spinning wheel initially has an angular velocity of 50 rad/sec East. 20 sec later its angular velocity is 50 rad/sec West. If the angular acceleration is constant, what are the

a)magnitude of the angular acceleration?

b)Angular displacement over 20 sec?

c)Angular speed after 30 sec?

  1. In 7 sec a car accelerates uniformly from rest to such speed that its wheels are turning at a rate of 6 rev/sec. What is the angular acceleration of the wheel? How many revolutions does the wheel undergo?
  1. Through how many revolutions must a 0.6 m diameter wheel of a car turn as the car travels 2500 m?
  1. Calculate the angular speed, frequency and linear speed of the second hand of a clock of needle length 0.02 m.
  1. An old phonograph record revolves at 45 rev/minute. What is the angular velocity in rad/sec?

a)0nce the motor is turned off, it takes 0.75 sec to come to a stop. What is its average angular acceleration?

b)How many revolutions did it make while coming to a stop?

  1. The Earth’s orbit around the Sun is almost a circle. With respect to the Sun, what are the Earth’s

a)angular speed

b)linear speed, if the radius of orbit is 1.5 x 1011 m

c)net force exerted by the sun on earth if mass of earth is 5.98 x 1024 kg

  1. If the radius of a long playing record is 0.15 m, at what linear speed would a particle of dust fly off, if the coefficient of static friction is 0.08? What would be the corresponding angular speed? At a distance halfway from the center what would be the required angular speed for the dust particle to fly off?
  1. If a man is diving from a cliff of height 44.1 m from the ground, how many revolutions can he make, if he is also spinning at a rate of 1.2 rev/sec?
  1. The drawing below shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance d = 1.250m, and rotating with an angular speed of 105 rad/s. The bullet traveling at 380 m/s passes through the left disk and then through the right disk. From this data, determine the angular displacement between the two bullet holes.

Bullet

d

  1. An electric grinder uses a 12 cm wheel. It takes the motor 3 sec to reach its rated speed of 1500 rev/minutes starting from rest. Find a) angular acceleration, b) the total angular displacement, c) the tangential velocity at the rim of the grinding wheel at maximum speed
  1. A car traveling at 30 m/sec has wheels with 75 cm diameters. Find a) angular speed of wheels, b) if the car stops in 5 sec, what is angular acceleration? C) how many revolutions do the wheels turn before stopping?
  1. A turn table takes 20 sec to reach a speed of 33.33 rev/minute. What are the a) angular acceleration, b) total # of revolutions before reaching final speed?