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A grinding wheel, initially at rest, rotates with a constant acceleration of 0.5 rad/s 2. At the instant that it has gone through an angular displacement.

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Presentation on theme: "A grinding wheel, initially at rest, rotates with a constant acceleration of 0.5 rad/s 2. At the instant that it has gone through an angular displacement."— Presentation transcript:

1 A grinding wheel, initially at rest, rotates with a constant acceleration of 0.5 rad/s 2. At the instant that it has gone through an angular displacement of 36 rad, what is its angular velocity? rad/s rad/s rad/s rad/s

2 A grinding wheel, initially at rest, rotates with a constant acceleration of 0.5 rad/s 2. What is the time interval required for it to reach a 36 rad displacement after starting from rest? s s s s

3 A 0.4 kg mass, attached to the end of a 0.75 m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N then what maximum velocity can the mass have if the string is not to break? m/s m/s m/s m/s

4 A 0.3 m radius automobile tire accelerates from rest at a constant 2 rad/s 2 over a 5 s interval. What is the tangential component of acceleration for a point on the outer edge of the tire during the 5 s interval? m/s m/s m/s m/s 2

5 A wheel rotating at the rate of 5 rev/s has what approximate angular velocity? rad/s rad/s 3.16 rad/s 4.31 rad/s

6 A military helicopter has rotor blades 3.0 m long rotating at 600 rpm. What is the tangential velocity of each blade tip? m/s m/s 3.33 m/s 4.66 m/s

7 A military helicopter has rotor blades 3.0 m long rotating at 600 rpm. What is the centripetal acceleration that must act 2.0 m from the axis of rotation? m/s m/s m/s m/s 2

8 A 0.3 m radius automobile tire rotates how many rad after starting at rest and accelerating at a constant 2 rad/s 2 over a 5 s interval? rad rad rad rad

9 A 0.3 m radius automobile tire accelerates from rest at a constant 2 rad/s 2 over a 5 s interval. What is the centripetal acceleration of a point on the outer edge of the tire at the end of the 5 s interval? m/s m/s m/s m/s 2

10 Geosynchronous satellites orbit the Earth at a distance of 42,000 km from the Earth's center. Their angular velocity at this height is the same as the rotation of the Earth, so they appear stationary at certain locations in the sky. What is the force acting on a 1500 kg satellite at this height? N N N N

11 The Earth is 93 million miles from the sun and its period of revolution is 1 year = 3.15 x 10 7 s. What is the orbital velocity of the Earth about the sun? miles/s miles/s miles/s miles/s

12 The escape velocity from the surface of the Earth is 11.2 km/s. Estimate the escape velocity for a spacecraft from the surface of the moon. The moon has a mass 1/81 that of Earth and a radius 1/4 that of Earth km/s km/s km/s km/s

13 For any object orbiting the sun, Kepler's Law may be written T 2 = kr 3. If T is measured in years and r in units of the Earth's distance from the sun, then k = 1. What, therefore, is the time (in years) for Mars to orbit the sun if its mean radius from the sun is 1.5 times the Earth's distance from the sun? years years years years

14 If the mass of Mars is times that of Earth and its radius is 0.53 that of Earth, estimate the gravitational acceleration g at the surface of Mars m/s m/s m/s m/s 2

15 An airplane in a wide sweeping "outside" loop can create zero gees inside the aircraft cabin. What must be the radius of curvature of the flight path for an aircraft moving at 150 m/s to create a condition of "weightlessness" inside the aircraft? m m m m

16 A cylindrical space colony 8 km in diameter and 30 km long has been proposed as living quarters for future space explorers. Such a habitat would have cities, land and lakes on the inside surface and air and clouds in the center. All this would be held in place by rotation of the cylinder about the long axis. How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder? radians/s radians/s radians/s radians/s

17 A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon. If the value of g on Io is 2 m/s 2, estimate the velocity with which the liquid sulfur left the volcano m/s m/s m/s m/s

18 What angular velocity (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1000 g at a radius arm of 15 cm? rev/s rev/s rev/s rev/s

19 According to Kepler's second law, Halley's Comet circles the sun in an elliptical path with the sun at one focus of the ellipse. What is at the other focus of the ellipse? Nothing 2.The Earth 3.The comet itself passes through the other focus. 4.The tail of the comet stays at the other ellipse.

20 Somewhere between the Earth and the moon is a point where the gravitational attraction of the Earth is canceled by the gravitational pull of the moon. The mass of the moon is 1/81 that of the Earth. How far from the center of the Earth is this point? /9 the way to the moon 2.9/10 the way to the moon 3.3/4 the way to the moon 4.80/81 the way to the moon

21 A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface. What is the velocity of the satellite? (The radius of the Earth is 6.4 x 10 6 m and G = 6.67 x N-m 2 /kg 2.) ,800 m/s 2.4,200 m/s 3.5,600 m/s 4.16,800 m/s

22 Calculate the linear speed due to the Earth's rotation for a person at the equator of the Earth. The radius of the Earth is 6.4 x 10 6 m m/s m/s m/s 4.73 m/s

23 If a planet has 3 times the radius of the Earth, but has the same density as the Earth, what is the gravitational acceleration at the surface of the planet? (g Earth = 9.8 m/s 2 ) m/s m/s m/s m/s 2

24 An object that is orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 1.00 N. What is the mass of this object? (The value of g at the surface of the Earth is 9.8 m/s 2 ) kg kg kg kg

25 What is the angular velocity about the center of the Earth for a person standing on the equator? x rad/s x rad/s x rad/s x rad/s

26 An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4000 miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface? There is no acceleration since the satellite is in orbit /2 4.1/4

27 Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular accelerations of the point Both are zero. 2.Only the angular acceleration is zero. 3.Only the linear acceleration is zero. 4.Neither is zero.

28 Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is upward. 2.down toward the ground. 3.forward. 4.at that moment the acceleration is zero.

29 Consider a child who is swinging. As she reaches the lowest point in her swing the tension in the rope is equal to her weight. 2.the tension in the rope is equal to her mass times her acceleration. 3.her acceleration is downward at 9.8 m/s 2. 4.none of these choices will occur.

30 Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point Both are constant. 2.Only the angular velocity is constant. 3.Only the linear velocity is constant. 4.Neither is constant.

31 A roller coaster, loaded with passengers, has a mass of 2000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? (g = 9.8 m/s 2 ) x 10 4 N x 10 4 N x 10 4 N x 10 4 N

32 A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.05 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s? rev/s rev/s rev/s rev/s

33 Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis. Compare the linear and angular displacement of the point Both are zero. 2.Only the angular displacement is zero. 3.Only the linear displacement is zero. 4.Neither is zero.

34 The end of the cutting cord on a gas-powered weed cutter is 0.15 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential velocity of the end of the cord? m/s 2.25 m/s 3.20 m/s 4.63 m/s

35 An object of mass 0.5 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4 x 10 6 m. What free fall acceleration will the 1.0 kg object experience when at the surface of Planet X? m/s m/s m/s m/s 2

36 An object of mass 0.5 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4 x 10 6 m. What free fall acceleration will the 0.5 kg object experience when transported to a distance of 2.0 x 10 6 m from the surface of this planet? m/s m/s m/s m/s 2

37 An object of mass 0.5 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4 x 10 6 m. What is the mass of Planet X? (g = 6.67 x N-m 2 /kg 2 ) x kg x kg x kg x kg

38 A 1500 kg car rounds an unbanked curve with a radius of 52 m at a speed of 12 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s 2 )

39 At what angle relative to the horizontal should a 52 m curve be banked if no friction were required to prevent the car from slipping when traveling at a speed of 12 m/s? (g = 9.8 m/s 2 ) ° 2.32° 3.16° 4.10°

40 At what speed would a car round a 52 m radius curve, banked at a 45° angle, where no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s 2 ) m/s 2.17 m/s 3.23 m/s 4.35 m/s

41 A 0.40 kg object is swung in a circular path and in a vertical plane on a 0.5 m length string. If a constant angular velocity of 8.0 rad/s is maintained, what is the tension in the string when the object is at the top of the circle? N N N N

42 A Ferris wheel, rotating initially at an angular velocity of 0.50 rad/s, accelerates over a 7 s interval at a rate of 0.04 rad/s 2. What angular displacement does the Ferris wheel undergo in this 7 s interval? rad rad rad rad

43 If the distance from the center of a Ferris wheel to the passenger seats is 12 m, what centripetal acceleration does a passenger experience when the wheel's angular velocity is 0.50 rad/s? m/s m/s m/s m/s 2

44 What centripetal force does an 80 kg passenger experience when seated 12 m from the center of a Ferris wheel whose angular velocity is 0.50 rad/s? N N N N

45 A 0.40 kg object is swung in a circular path and in a vertical plane on a 0.5 m length string. If the angular velocity at the bottom is 8.0 rad/s, what is the tension in the string when the object is at the bottom of the circle? N N N N

46 A Ferris wheel, rotating initially at an angular velocity of 0.50 rad/s, accelerates over a 7 s interval at a rate of 0.04 rad/s 2. What is its angular velocity after this 7 s interval? rad/s rad/s rad/s rad/s

47 A 0.15 m radius grinding wheel, starting at rest, develops an angular velocity of 12.0 rad/s in a time interval of 4 s. What is the average tangential acceleration of a point on the wheel's edge? rad/s rad/s rad/s rad/s 2

48 A 0.15 m radius grinding wheel, starting at rest, develops an angular velocity of 12.0 rad/s in a time interval of 4 s. What is the centripetal acceleration of a point 0.10 m from the center when the wheel is moving at an angular velocity of 12.0 rad/s? m/s m/s m/s m/s 2

49 A Ferris wheel, starting at rest, builds up to a final angular velocity of 0.7 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration? rad/s rad/s rad/s rad/s 2

50 A 0.15 m radius grinding wheel, starting from rest, develops an angular velocity of 12.0 rad/s in a time interval of 4 s. What is the wheel's average angular acceleration? rad/s rad/s rad/s rad/s 2

51 An artificial Earth satellite in an elliptical orbit has its greatest speed when it is at what location? nearest the Earth 2.farthest from the Earth 3.between Earth and moon 4.between Earth and sun

52 An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location? nearest the Earth 2.farthest from the Earth 3.between Earth and moon 4.between Earth and sun

53 Which of the following best describes the property of the period of orbital revolution for an Earth satellite? greater when the orbital radius is smaller 2.greater when the orbital radius is larger 3.independent of the orbital radius 4.determined mainly by the satellite's mass

54 Of the nine known planets in the solar system, the innermost one, Mercury, has which of the following? greatest centripetal acceleration 2.greatest period of revolution 3.smallest angular velocity 4.smallest tangential velocity

55 When a point on the rim of a 0.30 m radius wheel experiences a centripetal acceleration of 4.0 m/s 2, what tangential acceleration does that point experience? m/s m/s m/s 2 4.Cannot determine with information given.

56 A point on the rim of a 0.30 m radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.2 m from the center of the same wheel? m/s m/s m/s m/s

57 A point on the rim of a 0.20 m radius rotating wheel has a centripetal acceleration of 4.0 m/s 2. What is the centripetal acceleration of a point 0.05 m from the center of the same wheel? m/s m/s m/s m/s 2

58 A point on the rim of a 0.25 m radius rotating wheel has a centripetal acceleration of 4.0 m/s 2. What is the angular velocity of the wheel? rad/s rad/s rad/s rad/s

59 A point on the rim of a 0.20 m radius rotating wheel has a centripetal acceleration of 4.0 m/s 2. What is the angular velocity of a point 0.10 m from the center of the wheel? rad/s rad/s rad/s rad/s

60 Two satellites are monitored as they orbit the Earth; satellite X is eight times as far from the Earth's center as is satellite Y. From Kepler's third law one may conclude that the period or revolution of X is what factor times that of Y? /


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