Rotational Kinematics



Rotational Kinematics

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

a) 200

b) 0.40 rad

c) 1/3 rev

2. 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

3. 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?

4. 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?

5. 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?

6. 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?

7. Through how many revolutions must a 0.6 m diameter wheel of a car turn as the car travels 2500 m?

8. Calculate the angular speed, frequency and linear speed of the second hand of a clock of needle length 0.02 m.

9. 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?

10. 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

11. 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?

12. 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

2. 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

3. 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?

4. 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?

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Motor

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