Circular Motion Questions and Answers

When some stars use up their fuel they undergo a catastrophic explosion called a supernova This explosion blows much or all of the star s mass outward in the form of a rapidly expanding spherical shell As a simple model of the supernova process assume that the star is a solid sphere of radius R that is initially rotating at 2 0 revolutions per day After the star explodes find the angular velocity in revolutions per day of the expanding supernova shell when its radius is 4 0R Assume that all of the star s original mass is contained in the shell rev day

10 When a fan is turned off its an magnitude of the average angu

Describe the investigation you will conduct to find the relationship between the centripetal force and mass

A proposed space station includes living quarters in a circular ring 50 5 m angular speed should the in diameter At what rotate so the ring occupants feel that they have the same weight on Earth they do on

When an object moves in uniform circular motion, the direction of its acceleration is in the opposite direction of its velocity vector. depends on the speed of the object. is directed toward the center of its circular path. in the same direction as its velocity vector. is directed away from the center of its circular path.

A belt passes over a wheel whose radius is 45 cm. If a point on the belt has a velocity of 11.26 m/s, find the velocity the wheel is turning. Round your answer to 2 decimal places.

1. If a particle moves in a circle of radius R = 1.35 m at a constant speed of v= 6.70 m/s. what are the magnitude and the direction of its centripetal acceleration? Show your work and include units.

4. A 0.500 kg particle moves in a circle of radius R = 0.150 m at constant speed. The time for 20 complete revolutions is 31.7 s. (a) What is the period T of the motion? (b) What is the speed of the particle? (c) What is the centripetal acceleration of the particle? (d) What is the centripetal force on the particle? Show your work and include units.

3. If a particle of mass m=0.350 kg moves in a circle of radius R = 1.35 m at a constant speed of v= 6.70 m/s, what are the magnitude and direction of the centripetal force on it? Show your work and include units.

If a particle moves in a circle of radius R at constant speed v, its acceleration is (a) directed toward the center of the circle. (b) equal to v2/R (c) caused by the fact that the direction of the velocity vector changes continuously. (d) all of the above are true.

1. If a particle moves in a circle of radius R = 1.35 m at a constant speed of u = what are the magnitude and the direction of its centripetal acceleration? Show your work and include units.

When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s. (a) What is her angular speed in rad/s? (b) What is the magnitude of her linear acceleration?

A compact disk with a 12.0-cm diameter is rotating at 31.6 rad/s. Part C Consider a point on the CD that is halfway between its center and its outer rim. Without repeating all of the calculations required for part A, determine the linear speed at this point. Express your answer using three significant figures.

A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 11.0 s before coming to rest. If its initial angular speed was 3900 rpm, what is the magnitude of its angular deceleration?

A corn is placed on the horizontal surface of a rotating disc. The distance of the coin from the axis is I m and coefficient of friction is 0.5. If the disc starts from rest and is given an angular acceleration 1/√2 rad/sec² the number of revolutions through which the disc turns the coins slips in:

As Tony the fisherman reels in a "big one," he turns the spool on his fishing reel at the rate of 2.8 complete revolutions every second. ▼ Part A If the radius of the reel is 3.2 cm, what is the linear speed of the fishing line as it is reeled in? Express your answer using two significant figures.

6. During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm. a. Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel. b. Determine the acceleration of the clothes.

What is the angular velocity of the minute hand of a clock? Hint: It travels clockwise and takes 60 minutes to make one revolution.

A 0.300-kg mass, attached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break? 22.4 m/s 19.4 m/s 25.0 m/s 32.7 m/s

A car of mass 1.5x103 kg rounds a circular turn of radius 20 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.50, how fast can the car travel without skidding?

A car is negotiating a flat circular curve of radius 70 m with a speed of 29 m/s. The maximum centripetal force (provided by static friction) is 1.2 × 104 N. What is the mass of the car? 1.5 × 10³ kg 0.50 × 10³ kg 1.0 x 10 kg 2.0 × 10³ kg

The rotational velocity of a spinning disk decreases from 13.3 rev/sec to 4 rev/sec in a time of 10 s. (a) What is the rotational acceleration of the disk?

A 200 g block on a 56.0 cm -long string swings in a circle on a horizontal, frictionless table at 50.0 rpm Part A What is the speed of the block? Express your answer with the appropriate units. Part B What is the tension in the string? ?

Starting from rest, a merry-go-round accelerates at a constant rate of 18 rev/s2. (a) What is its rotational velocity after 1.3 s? (b) How many revolutions occur in this time?

3. A circular racetrack has a radius of 500 meters. Cars start at a starting line and drive clockwise around the track. At 1/3rd the distance of the track from the starting line is the first checkpoint. a. In radians, what angle needs to be travelled by the racers from the start to the first checkpoint? b. How much physical distance do the racers travel in part a? c. The fastest car reaches the first checkpoint in 18.6 seconds. Over that time period, what was their average angular velocity? d. Over the time period in part c, what was the fastest car's average linear velocity? e. Assuming the car keeps the same velocity as your answer to part d, what would its centripetal acceleration be? f. What force is causing this centripetal acceleration?

The around the world yo-yo trick is completed when you twirl a yo-yo in a vertical circle. If the yo-yo was in uniform circular motion, compare the force of tension at the top of the circle to the force of tension at the bottom of the circle. Hint: Drawing a free body diagram will be helpful.

A level circular track has a radius of 121 meters. A 760-kilogram car moves around the track with a constant linear speed of 28 meters per second. What coefficient of static friction between the tires and the track is required to keep the car from sliding sideways?

A 0.550-kilogram ball attached to a string swings along a circular path of radius 0.250 meter, as shown. The instantaneous linear speed of the ball is 2.15 meters per second. What is the tension in the string? (a) 11.5 N (b) 10.8 N (c) 7.19 N (d) 5.40 N E 1 0.250 m

(II) (a) A grinding wheel 0.35 m in diameter rotates at 2200 rpm. Calculate its angular velocity in rad/s. (b) What are the linear speed and acceleration of a point on the edge of the grinding wheel?

Tarzan (mass m = 80.0 kg) crosses a river by swinging on a vine. The vine (negligible mass) is 10.0 m long. If Tarzan's speed at the bottom of his swing is 5.0 m/s and the acceleration of gravity is 10 m/s2, then the tension in the vine will be O a. 1300 N b. 1400 N O c. 1000 N d. none of these e. 784 N

The maximum speed that a 950-kg car can round a curve of radius 53 m on a flat, but wet, road if the coefficient of static friction between the tires and the road is equal to 0.70 is Oa. 13 m/s b. 19 m/s O c. 36 m/s d. 22 m/s Oe. none of these

A set of keys on the end of a string is swung steadily in a horizontal circle. In one trial, it moves at speed v in a circle of radius r. In a second trial, it moves at a higher speed 4v in a circle of radius 4r. In the second trial, how does the period of its motio compare with its period in the first trial? It is one-sixteenth as large. It is 16 times larger. It is one-fourth as large. It is 4 times larger. It is the same as in the first trial.

An automobile engine slows down from 3500 rpm to 1200 rpm in 2.5 s. Calculate (a) its angular acceleration, assumed constant, and (b) the total number of revolutions the engine makes in this time.

A 0.60-kg rock is swung in a circular path and in a vertical plane on a 0.50-m-length string. At the top of the path, its speed is 4 m/s. What is the tension in the string at that point?

A wheel, rotating initially at an angular speed of 0.50 rad/s, decelerated over a 7.0-s interval at a rate of 0.040 rad/s². What is its angular speed after this 7.0-s interval? What is the angular displacement?

A communications satellite forms a circular orbit 235 mi above the earth. If the earth's radius is approximately 4,000 mi, what distance (in miles) is traveled by the satellite in one complete orbit?

A father fashions a swing for his kids out of a long rope that he fastens to the limb of a tall tree. As one of the kids swings from this rope that is 7.00 m long his tangential speed at the bottom of the swing is 9.30 m/s. What is his angular speed in rad/s?

You are playing an old 78.0 rpm album when you notice a small piece of lint on the record at a distance of 6.7 cm from the center of the turntable. Light coming in through the window (essentially parallel rays) casts a shadow of the lint on the wall behind the turntable. Determine the maximum speed of the lint's shadow on the wall.

Block A of mass 5kg is kept on another block B of mass 10kg, which is placed on a horizontal platform P. Assume acceleration due to gravity 10m/s² and magnitude of normal reactions between the blocks A and B is N₁ and between the block B and the platform is N₂. When the platform is moving downward with acceleration 10 m/s², N₁ = N₂ = zero. When the platform is moving upward with uniform velocity of 5 m/s, N₁ = 50 N & N₂ = 150 N. When the platform is moving upward with acceleration 5 m/s², N₁ = 75N & N₂ = 225N. When the platform is moving downard with uniform velocity of 5 m/s, N₁ = 50 N & N₂ = 150 N.

An electric motor rotating a workshop grinding wheel at a rate of 1.35 x 102 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.10 rad/s². (a) How long does it take for the grinding wheel to stop? S (b) Through how many radians has the wheel turned during the interval found in (a)? rad

A small cart of mass m = 0.755 kg is moving at a constant speed v = 8.75 m/s on the inside of a vertical circular track with radius 4.35 m. (a) Calculate the period of the cart's motion. (b) Calculate the normal force (in Newtons) that the track exerts on the cart at its topmost point. (c) If the track wasn't there but the cart was moving with the same speed, period, and radius around an object in the center of the circle, purely due to the gravitational attraction between them, calculate the mass of that object in the center.

A Ferris wheel with radius of 14.0 m is turning about a horizontal axis through its center. The linear speed of a passenger on the rim is constant and equal to 7.00 m/s. (a) What are the magnitude and direction of the passenger's acceleration as she passes through (i) the lowest point in the circular motion; (ii) the highest point in the circular motion; and (iii) the point halfway between the highest and the lowest point? (b) What is the magnitude of the normal force that the Ferris wheel exerts on this passenger (m = 70.0 kg) at each of the three points described in (a)? (c) How much time does it take the Ferris wheel to make one revolution?

What is the angular acceleration of the wheels of a car that is traveling at a constant velocity 60 km/hr? a=v/t a. zero b. 15 km/hr/sec c. 30 km/hr/sec d. 60 km/hr/sec

Medical cyclotrons need efficient sources of protons to inject into their center. In one kind of ion source, hydrogen atoms (i.e., protons with one orbiting electron) are fed into a chamber where there is a strong magnetic field. Electrons in this chamber are trapped in tight orbits, which greatly increases the chance that they will collide with a hydrogen atom and ionize it. One such source uses a magnetic field of 90 mT, and the electrons' kinetic energy is 1.2 eV. If the electrons travel in a plane perpendicular to the field, what is the radius of their orbits? (mₑ =9.11x 10⁻³¹kg, qₑ = 1.60 x 10⁻¹⁹ C, 1eV = 1.6 x 10⁻¹⁹ J) Express your answer in meters to two significant figures.

An athlete swings a 3.10-kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.650 m at an angular speed of 0.620 rev/s. (a) What is the tangential speed of the ball? (b) What is its centripetal acceleration? (c) If the maximum tension the rope can withstand before breaking is 119 N, what is the maximum tangential speed the ball can have?

A mass m1 (3.0 kg) is connected by a light string that passes over a pulley of mass M(40 kg to a mass m2 (2.0 kg) sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of % MR^2? The angle is 60 degrees, then what is the acceleration of m1? 2.8 m/s2 2.2 m/s2 1.2 m/s2 0.0 m/s2 1.8 m/s2

A 25 kg child moves with uniform circular motion while riding a horse on a carousel. The horse is 4.2 m from the carousel's axis of rotation and has a tangential speed of 3.6 m/s. What is the child's centripetal force?

When a car goes around a curve of radius r at a constant speed v. it is acted upon by a centripetal force of 1.0 kN. When the same car goes around a curve of radius 3r at speed 2v, what would be the centripetal force acting on the car? a. 1.0 kN b. 0.66 kN c. 1.3 kN d. 0.75 kN

Mary is driving a car around a circular racetrack, which has a diameter of six miles. It takes her a half hour to make one full revolution around the track. If Mary is not speeding up or slowing down, what is Mary's instantanious speed? What is Mary's average speed?

An object of mass 6.0 kg is whirled around in a vertical circle on the end of a 1.0 m long string with a constant speed of 8.0 m/s. Include a free-body diagram for each of the following questions: a. Determine the maximum tension in the string, indicating the position of the object at the time the maximum tension is achieved. b. What is the minimum speed the object could be rotated with and maintain a circular path? c. If the object is rotated with the same speed (8.0 m/s) on a horizontal surface, what is the tension in the string if the string is parallel to the surface?