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Circular motion and gravity exercises · Physics Playground

ExercisesPhysics

Circular motion and gravity

18 problems with worked solutions, from Physics and College Physics.

Start with a random one

Learn it first: Circular Motion, Gravity & Orbits

Physics6.1 Angle of Rotation and Angular Velocity

ExampleAngle of rotation at a Clock TowerThe clock on a clock tower has a radius of 1.0 m. (a) What angle of rotation does the hour hand of the clock travel through when it moves from 12 p.m. to 3 p.m.? (b) What’s the arc length along the outermost edge of…
ExampleHow Fast Does a Car Tire Spin?Calculate the angular speed of a 0.300 m radius car tire when the car travels at 15.0 m/s (about 54 km/h). See Figure 6.5.

Physics6.2 Uniform Circular Motion

ExampleComparing Centripetal Acceleration of a Car Rounding a Curve with Acceleration Due to GravityA car follows a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h). What is the magnitude of the car’s centripetal acceleration? Compare the centripetal acceleration for this fairly gentle curve taken at…With a figure
ExampleFrictional Force on Car Tires Rounding a CurveCalculate the centripetal force exerted on a 900 kg car that rounds a 600-m-radius curve on horizontal ground at 25.0 m/s. Static friction prevents the car from slipping. Find the magnitude of the frictional force…With a figure

Physics6.3 Rotational Motion

ExampleCalculating the Time for a Fishing Reel to Stop SpinningA deep-sea fisherman uses a fishing rod with a reel of radius 4.50 cm. A big fish takes the bait and swims away from the boat, pulling the fishing line from his fishing reel. As the fishing line unwinds from the…With a figure
ExampleCalculating the Torque on a Merry-Go-RoundConsider the man pushing the playground merry-go-round in Figure 6.11. He exerts a force of 250 N at the edge of the merry-go-round and perpendicular to the radius, which is 1.50 m. How much torque does he produce?…

Physics7.1 Kepler's Laws of Planetary Motion

ExampleKepler’s First LawAt its closest approach, a moon comes within 200,000 km of the planet it orbits. At that point, the moon is 300,000 km from the other focus of its orbit, f2. The planet is focus f1 of the moon’s elliptical orbit. How…
ExampleKepler’s Second LawFigure 7.6 shows the major and minor axes of an ellipse. The semi-major and semi-minor axes are half of these, respectively. Figure 7.6 The major axis is the length of the ellipse, and the minor axis is the width of…With a figure
ExampleKepler’s Third LawGiven that the moon orbits Earth each 27.3 days and that it is an average distance of 3.84× 10 ^8 m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1,500…

Physics7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity

ExampleChange in gThe value of g on the planet Mars is 3.71 m/s2. If you have a mass of 60.0 kg on Earth, what would be your mass on Mars? What would be your weight on Mars?
ExampleEarth’s g at the MoonFind the acceleration due to Earth’s gravity at the distance of the moon. G = 6.67 × 10^(–11) N · m^2 /kg^2 Earth-moon distance = 3.84 × 10^8 m Earth’s mass = 5.98 × 10^(24) kg 7.5 Express the force of gravity in…

College Physics6.1 Rotation Angle and Angular Velocity

Example 6.1How Fast Does a Car Tire Spin?Calculate the angular velocity of a 0.300 m radius car tire when the car travels at 15.0m/s (about 54km/h). See Figure 6.5.

College Physics6.2 Centripetal Acceleration

Example 6.2How Does the Centripetal Acceleration of a Car Around a Curve Compare with That Due to Gravity?What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve…
Example 6.3How Big Is the Centripetal Acceleration in an Ultracentrifuge?Calculate the centripetal acceleration of a point 7.50 cm from the axis of an ultracentrifuge spinning at 7.5 × 10^4 rev/min. Determine the ratio of this acceleration to that due to gravity. See Figure 6.9(b).

College Physics6.3 Centripetal Force

Example 6.4What Coefficient of Friction Do Car Tires Need on a Flat Curve?(a) Calculate the centripetal force exerted on a 900 kg car that negotiates a 500 m radius curve at 25.0 m/s. (b) Assuming an unbanked curve, find the minimum static coefficient of friction, between the tires and the…
Example 6.5What Is the Ideal Speed to Take a Steeply Banked Tight Curve?Curves on some test tracks and race courses, such as the Daytona International Speedway in Florida, are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the…

College Physics6.5 Newton’s Universal Law of Gravitation

Example 6.6Earth’s Gravitational Force Is the Centripetal Force Making the Moon Move in a Curved Path(a) Find the acceleration due to Earth’s gravity at the distance of the Moon. (b) Calculate the centripetal acceleration needed to keep the Moon in its orbit (assuming a circular orbit about a fixed Earth), and…

College Physics6.6 Satellites and Kepler’s Laws: An Argument for Simplicity

Example 6.7Find the Time for One Orbit of an Earth SatelliteGiven that the Moon orbits Earth each 27.3 d and that it is an average distance of 3.84×10^8m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1500 km above…