Circular, Periodic and Rotational Motion

Name: Yr. & Section:

Date: Score: Circular, Periodic, and Rotational Motion

1. A car rounds a flat curve on the highway that has a radius of 200 m, making a 90 degree-turn at a speed of 22.0 m/s. What is the minimum coefficient of kinetic friction to prevent skidding at this speed? Fc = Fk 2. The moon completes one revolution around the Earth in 27 .3 days. Calculate the centripetal 8

acceleration of the moon. The radius of the moon’s orbit is 3.84 x 10  m. 3. How long does it take a 50 kg runner to run a circular track starting and ending at the same point, if the radius of the track is 30 m? A centripetal force of 68 N keeps him running at constant speed in a circular path. 4. A 400 g rock attached to a 1.0 m string is whirled in a horizontal circle at the constant speed of 10.0 m/s. Neglecting the effects of gravity, what is the centripetal force acting on the rock? 5. A little girl is playing with her foot j ump. The ball in her foot jump is in uniform circular motion and makes 20 revolution in 4 seconds. a. What is its period? b. What is its frequency? c.

If the length of the plastic cord that holds the ball is 0.87 m, w hat is the speed of the ball?

d. If the ball has a mass of 4 g, how much force is acting on the ball to keep it in uniform circular motion? 6. Young David who slew Goliath experimented with slings before tackling t he giant. He found that he could revolve a sling of length 0.600 m at the rate of 8.00 rev/s. if he increased the length t o 0.900 m, he could revolve the sling o nly 6.00 times per second. a. Which rate of rotation gives the greater speed for the stone at the end of the sling? b. What is the centripetal acceleration of the stone at 8.00 rev/s? c.

What is the centripetal acceleration at 6.00 rev/s?

7. A curve of 183 m radius on a level road is banked at the correct angle for a velocity veloc ity of 13.4 m/s. If an automobile rounds this curve at 26.8 m/s, what is the minimum coefficient of friction between the tires and road so that the automobile will not skid? 8. A car is to make a turn with a radius of curvature of 6 0 m at a speed o f 27 m/s. At what angle should the road be banked for the car to make the turn? 9. A car is traveling at 9 m/s in a circle that has a radius 60 m. What must be the minimum value of coefficient of friction for the car to make the turn without skidding?

Name: Yr. & Section:

Date: Score:

10. A rotating room has a radius of 4 .5 m and the speed of the rider is 12 m/s. How much should the 2

coefficient of static friction (µ= rg/v ) be to keep the rider pinned against the wall? 11. Convert the following into the indicated units: a) 310° to rad b) 560 rad to rev c) 33 rad to deg. d) 2π/5 rad to deg. 12. Convert the following into the indicated units: a) 16 rad to deg. b) 755 rev to deg. c) 55° to rad d) π/7 rad to deg 13. A 65-kg pilot is flying a small plane 35 m/ s in a circular path with a radius of 11 000 cm. What is the force that keeps the circular motion of the pilot? 14. The maximum force a road can exert on the tires of a 1600-kg car is 8400 N. What is the maximum velocity at which the car can round a turn of radius 130 m? 15. Merry-go-round is rotating at a constant angular velocity of 2 .5 rad/s. What is the frequency of the merry-go-round in revolutions per minute? 16. A 1000-kg car rounds a turn of radius 2500 cm at a v elocity of 8 m/s. a) How much centripetal force is needed? b) Where does this force come from? 17. A figure skater begins spinning counterclockwise at an angular speed of 5π rad/s. she slowly pulls her arms inward and finally spins at 9π rad/s for 3.0 s. What is her average angular acceleration during this time interval? 18. A fish swimming behind a luxury cruise liner gets caught in a whirlpool created by the ship’s propeller. If the fish has an angular velocity of 1 .5 rad/s and the water in the whirlpool 2

accelerates at 3.5 rad/s , what will be the instantaneous angular velocity of the fish at the end of 4.0 seconds? 19. A boy rides on a merry-go-round at a distance of 1.25 m from the center. If the boy moves through an arc length of 2.25 m, through what angular displacement does he move? 20. A child in a barber shop spins on a stool. I f the child turns counterclockwise through 8.0πrad during an 8.0 s interval, what is the average angular velocity of the child’s rotation? 21. A compass draws a circle on a piece of paper 30 cm in circumference. What was the distance of the needle to the pen of the compass when the circle was drawn? What is the diameter of the circle drawn?

Name: Yr. & Section:

Date: Score:

22. A wheel of radius 14.0 cm starts from rest and turns through 2.0 revolutions in 3.0 s. What is its average angular velocity? What is the t angential velocity of a point on the rim of the whee l? 23. A phonograph turntable initially rotating at 3 rad/s makes four complete turns before coming to a stop. What is its angular acceleration? 24. Many amusement parks feature a ride wherein a giant ship swings back and forth. If the period of the ship is 7.0 s, what is the frequency of the swinging ship? 25. What is the frequency of an acrobat swinging on a trapeze if the c ables are approximately 2.5 m long? 26. An acrobat swings from a trapeze w ith a frequency of 0.5 Hz. What is the length of the trapeze cable? 27. How long should a simple pendulum be to have a period o f one second? A tire 0.500 m in radius rotates at a constant rate of 200 rev/min. Find the speed and acc eleration of a small stone in the thread of the tire (on its outer edge). 6

28. In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.20 x 10

-

m/s. Find: a) the force acting on the electron as it revolves in a circular orbit of radius 0.530 x 10 10

 m and b) the centripetal acceleration of the electron.

29. Determine the distance between two cities along the equator whose longitudes corre sponds to 6

75° and 76°. Consider the radius of the earth as 6.38 x 10 m. 30. The earth makes one rotation about its axis in 24 hours. A) Calculate the angular velocity in units of rad/s. b) calculate the tangential speed of an object at the equator due to this motion of the earth. 31. Calculate the centripetal acceleration of a car traveling on a circular racetrack of radius 1000-m at a speed of 180 kph. 32. A 1.2 –kg block slides on a horizontal frictionless surface in a c ircular path at the end of a 0.50-m string. Calculate the block’s speed if the tension in the string is 86 N. 33. A ball is fastened to one end of a 24-cm string, and the other end is held fixed above. The ball is whirled in a horizontal circle. Find the speed of the ball in its circular path if the string makes an angle of 30° to the vertical. 34. A bicycle tire of radius 0.68 m rotates 1,000 times in 600 s. Calculate a0 the distance traveled by the valve system, b) its average tangential speed, and c) its average angular velocity.

Name: Yr. & Section:

Date: Score:

35. A wheel is 1 meter in diameter. When it makes 30 rev/min angular velocity, the tangential speed of a point on its circumference is? 36. A bicycle starts from rest and 10 s later has an angular velocity of 2.5 rev/s. Calculate its average angular acceleration during those 10 seconds. 2

37. A flywheel undergoes an average angular accelerat ion of 1.50 rad/s . a) Calculate the average tangential acceleration of its valve system, which is 0.68 m from the axis of rotation. b) Calculate the valve system’s tangential speed after 10s, if it starts from rest. 38. A bicycle wheel makes 500 rpm. Determine the period of the wheel in seconds. 39. Suppose the wheel of a bicycle whe el makes 5 revolutions in 1 min, what is its frequency in rps? 40. A 0.2 kg metal ball is tied to a string 0.6 m long. If the breaking strength of the string is 66.74 N, determine the maximum speed with which the stone can be whirled in a horizontal circle.

Note: Tangential speed –actual speed of the object moving in a circle Tangential acceleration – the actual acceleration of the object moving in a circle. Rps - revolution per second Rpm - revolution per minute

Name: Yr. & Section:

Date: Score:

CHAPTER 3: CAPACITANCE a. CAPACITANCE - is a measure of the capacity of storing electric charge for a given potential difference ∆V . b. CAPACITOR - a device for storing electrical charges - a combination of conducting plates separate d by an insulator or dielectric. C. The Parallel- Plate Capacitor - most common type of capacitor consist of two conducting plates parallel to each other separated by a distance that is small compared with the linear dimensions of the plate. - the entire field of such a capacitor is localized in the region between the plates, the fields between the plates are uniformly distributed over their opposing surfaces.