**Option 1**

1) A wheel makes 30 revolutions in 2 minutes. Determine the period and frequency of rotation.

2) A cyclist moves along a curve of a road with a radius of 50 m at a speed of 36 km/h. At what acceleration does he pass the curve?

3) Calculate the first cosmic velocity to be given to an artificial satellite of the Earth near its surface. The mass of the Earth is 6∙1024 kg, its radius is 6400 km.

4) With what force, directed horizontally, does a streetcar car weighing 24 t press on the rails if it moves along a curve of radius 100 m at a speed of 18 km/h?

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**Option 2**

1) A wheel makes 90 revolutions in 3 minutes. Determine the period and frequency of rotation.

2) At what speed does a cyclist travel around a cycle track with a radius of 50 m if he has a centripetal acceleration of 2 m/s2?

3) Calculate the first cosmic velocity that should be given to an artificial satellite of the Earth at an altitude equal to 2Rz. The mass of the Earth is 6∙1024 kg, the radius of the Earth is 6400 km.

4) An airplane makes a dead loop with radius 225 m and has speed 50 m/s. With what force will the pilot, whose mass is 80 kg, press on the seat at the lower point of the loop?

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**Option 3**

1) A body moves on a circle of radius 10 m. The period of its revolution is 20s. What is the speed of the body?

2) A train moves at a speed of 72 km/h along a roundabout. Determine the radius of the arc if the centripetal acceleration of the train is 0.5 m/s2.

3) Calculate the first space velocity at an altitude of 3R from the Earth’s surface. Take the average radius of the Earth to be 6400 km.

4) A body with mass 20 g moves along a circle of radius 0.2 m with a speed of 90 m/s. Determine the force acting on the body.

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**Option 4**

1) A body moves on a circle of radius 5 m with a speed of 20 m/s. What is the frequency of revolution?

2) A car moves along a circle of the road with a radius of 20 m/s with centripetal acceleration of 5 m/s2. What is the velocity of the car ?

3) Calculate the first space velocity for the Moon if its mass is 7-1019 t and its mean radius is 1730 km.

4) A railroad car with a mass of 10 t moves along a curve with a radius of 250 m at a speed of 36 km/h. Determine the force acting on the wagon.

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**Option 5**

1) A car on a curve moves along a circle of radius 16 m at a constant speed of 36 km/h. What is the centripetal acceleration?

2) A streetcar car moves along a circle of radius 20m. Determine the speed of the streetcar if the centripetal acceleration is 0.5 m/s2.

3) Calculate the first cosmic velocity at height 1.5R of Earth from Earth’s surface. Take the average radius of the Earth to be 6400 km.

4) A car with a mass of 1 t moves along a circle of radius 100 m. Determine the force acting on the car at a speed of 36 km/h.

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**Option 6**

1) A body moves on a circle of radius 5m. The period of its revolution is 10s. What is the speed of the body?

2) A car makes a turn at a speed of 43.2 km/h along an arc with a radius of 60 m. Determine the centripetal acceleration.

3) A dump truck with a mass of 15 t moves at a speed of 36 km/h along a curve with a radius of 50 m. Determine the force acting on the dump truck.

4) Calculate the first space velocity for Venus if its mass is 4.9-1021 t and average radius is 3025 km.

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**Option 7**

1) A body moves on a circle of radius 6 m. The period of its revolution is 14s. What is the speed of the body?

2) A motorcyclist moves along a circle of radius 50 m with a speed of 5 m/s. Determine the centripetal acceleration of the motorcyclist.

3) A streetcar car with a mass of 6 t is traveling at a speed of 18 km/h along a circle of radius 100 m. Determine the force acting on the carriage.

4) Calculate the first space velocity for Mercury if its mass is 6.44-1023 kg and its mean radius is 3390 km.

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**Option 8**

1) What is the speed of a train if the wheels of a locomotive with a radius of 1.2m make 160 rpm?

2) What is the speed of a body moving uniformly on a circle of radius 3 m, if the centripetal acceleration is 12 cm/s2?

3) A car with a mass of 1 ton is moving along a circle with a radius of 100 m. Determine the force acting on the car at a speed of 36 km/h.

4) Calculate the first space velocity for Venus if its mass is 3.3-1023kg and its average radius is 2440 km.

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**Option 9**

1) A body moves on a circle of radius 10 m. The period of its rotation is 20s. What is the speed of the body?

2) A cyclist moves along a rounded section of road with a radius of 100m at a speed of 10m/s. Determine the centripetal acceleration?

3) A car weighing 5 tons travels over a convex bridge at a speed of 21.6 km/h. With what force it presses on the middle of the bridge having radius of curvature of 50 m?

4) What speed should an artificial satellite of the Moon have in order to orbit the Moon in a circular orbit at an altitude of 40 km? The acceleration of gravity for the Moon at this altitude is 1.6 m/s2 and the radius of the Moon is 1760 km.