Physics Problems: Uniform Circular Motion and Gravitation PDF Lecture 06

Lecture 06 Uniform Circular Motion and Gravitation A wind turbine for generating electricity rotates clockwise at the rate of 17.0 rpm (revolutions per minute). What is its angular velocity in rad/s? A CD rotates at a constant speed through an angle of 106° in 0.0860 𝑠. What is the angular veloci...

Lecture 06 Uniform Circular Motion and Gravitation A wind turbine for generating electricity rotates clockwise at the rate of 17.0 rpm (revolutions per minute). What is its angular velocity in rad/s? A CD rotates at a constant speed through an angle of 106° in 0.0860 𝑠. What is the angular velocity of the CD in rad/s? Find the period of a microwave tray rotating with an angular speed of 5.0 rpm. The centrifuge shown in the figure rotates counterclockwise at the rate that gives the bottom of the test tube a linear speed of 90.6 m/s. If the test tube is 9.25 cm from the axis of rotation, what is the centripetal acceleration experienced there? A 1200 kg car rounds a corner of radius r = 45 m. If the coefficient of static friction between the tires and the road is 𝜇𝑠 = 0.82, what is the greatest speed the car can have in the corner without skidding? If a roadway is banked at the proper angle, a car can round a corner without any assistance from friction between the tires and the road. Find the appropriate banking angle for a 900 kg car traveling at 20.5 m/s in a turn of radius 85.0 m. A sled with a mass of 25.0 kg rests on a horizontal sheet of essentially frictionless ice. It is attached by a 5.00 m rope to a post set in the ice. Once given a push, the sled revolves uniformly in a circle around the post, making five complete revolutions every minute. Find the force exerted by the rope on the sled, the acceleration and the speed. A passenger on a carnival Ferris wheel moves in a vertical circle of radius R with constant speed v. The seat remains upright during the motion. Find expressions for the force the seat exerts on the passenger when (a) at the top of the circle and (b) when at the bottom. As part of a circus act, a person drives a motorcycle with constant speed v around the inside of a vertical track of radius r. If the combined mass of the motorcycle and rider is m, find the normal force exerted on the motorcycle by the track at points (a) A, (b) B, and (c) C. An inventor designs a pendulum clock using a bob with mass m at the end of a thin wire of length L. Instead of swinging back and forth, the bob is to move in a horizontal circle at constant speed v, with the wire making a fixed angle 𝜷 with the vertical direction. This is called a conical pendulum because the suspending wire traces out a cone. Find the tension T, the centripetal acceleration acp, and its angular velocity 𝝎. Two apples of mass m1 = 0.110 kg and m2 = 0.220 kg sit on a dining room table. Treating the apples as point objects, find the force of gravity between them when their separation is 13.2 cm. Many stars belong to systems of two or more stars held together by their mutual gravitational attraction. The figure shows a three-star system when the stars are at the vertices of a right triangle of size d1 = 3 × 1012 m and d2 = 4 × 1012. Find the total gravitational force exerted on star A (mass 3 × 1030 kg), by star B (mass 8 × 1030 kg) and star C (mass 10 × 1030 kg). If you climb to the top of Mt. Everest, you will be about 5.50 mi above sea level. What is the acceleration due to gravity at this altitude? (a) Find the acceleration due to gravity on the surface of the Moon. The mass of the Moon is 𝑀𝑚 = 7.34 × 1022 kg and its radius is 𝑅𝑚 = 1.74 × 106 m. (b) The lunar rover had a mass of 225 kg. What was its weight on the Earth and on the Moon? After landing on Mars, an astronaut performs a simple experiment by dropping a rock. A quick calculation using the drop height and the time of fall yields a value of 3.73 m/s 2 for the rock's acceleration. (a) Find the mass of Mars, given that its radius is 𝑅𝑀 = 3.39 × 106 m. What is the acceleration due to gravity at a distance 𝑟 = 2𝑅𝑀 from the center of Mars? The Earth revolves around the Sun once a year at an average distance of 1.50 × 1011 m. (a) Use this information to calculate the mass of the Sun. (b) Find the period of revolution for the planet Mercury, whose average distance from the Sun is 5.79 × 1010 m.