Rotational Kinematics Unit Worksheet
Learning Goals:
I can solve circular kinematics problems
I can calculate centripetal force
I can solve problems involving friction and centripetal force
1. A carnival swing is fixed on the end of an 8.0 m long beam. If the swing and beam sweep through an angle of 120o, what is the distance through which the riders move? (17 m)
2. A mosquito lands on a phonograph record 5.0 cm from the record’s center. If the record turns clockwise so that the mosquito travels along an arc length of 5.0 cm, what is the angular displacement? (-1.0 rad)
3. What would the angular displacement of a car tire be if its diameter were 37.0 cm and moved through an arc length of 110.0 cm? (5.95 rad)
4. A bicyclist rides along a circular track. If the bicyclist travels around exactly half the track in 10.0 s, what is his average angular speed? (0.314 rad/s)
5. Find the average angular speed of the second hand of a clock. (0.105 rad/s)
6. A wheel is rotating at a rate of 2.0 revolutions every 3.0 s. Through what angle in radians, does the wheel rotate in 1.0 s? (4.2 rad)
7. Find the angular acceleration of a spinning amusement-park ride that initially travels 0.50 rad/s then accelerates to 0.60 rad/s during a 0.50 time interval. (0.20 rad/s2)
8. A drill starts from rest. After 3.20 s of constant angular acceleration, the drill turns at a rate of 2628 rad/s. What is the angular acceleration? What is the angle through which the drill rotates during this period? (821.3 rad/s2, 4200 rad)
9. A tire placed on a balance machine in a service station starts from rest and turns through 4.7 revs in 1.2 s before reaching its final angular speed. Assuming that the angular acceleration of the wheel is constant, calculate the wheel’s angular acceleration. (41 rad/s2)
10. A small pebble is lodged into a tire that has a diameter of 0.50 m. While in motion, the tire makes 12 revolutions in 3.0 seconds. If the pebble breaks loose from the treads, what will its linear speed be? (6.3 m/s)
13. A 45 kg man is standing on the equator of Earth. If the radius of Earth is 6.4 x 106m, what is the linear speed of the man? (470 m/s)
14. Find the average angular speed of the Earth about the sun in radians per second. If the distance between the Earth and sun is 1.496 x 1011m, what is the Earth’s linear speed? (1.991 x 10-7 rad/s, 29 800 m/s)
15. A computer hard drive has a rotational speed of 7200 rpm. What is the angular speed? What is the frequency of this hard drive? (750 rad/s, 120 Hz)
16. A DVD is spinning with a frequency of 250 Hz. What is the angular speed of this DVD? (1600 rad/s)
17. A plane is flying in a circle that has a circumference of 2.00 103m with a linear speed of 255 m/s. What is the plane’s angular speed? What is the plane’s radial acceleration? (0.802 rad/s, 204 m/s2)
18. In a popular amusement-park ride, a cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider’s clothing and the wall of the cylinder is needed to keep the rider from slipping? (0.131)
19. What is the centripetal force that holds the moon in orbit? Mass of moon = 7.36 x 1022 kg, distance of 3.828 x 108 m between Earth and moon, moon’s period is 29.53059 days. (1.71 x 1020N)
20. A 1700.0 kg truck is driven along a circular entrance ramp with a radius of 60.0 m at a constant rate of 20.0 m/s. What must the coefficient of friction between the tires and the road be to keep the truck on the road? (0.680)
21. a 2.00 x 103 kg car rounds a circular turn of radius 20.0 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.700, how fast can the car go without skidding? (11.7 m/s)