College Physics
OER 2016 Edition
ISBN: 9781947172173
Author: OpenStax
Publisher: OpenStax College
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Chapter 10, Problem 7TP
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A space probe in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope is I = 17.5 kg m² about the axis of the gyroscope, and the moment of inertia of the rest of the space probe is I = 5.00 × 105 kg • m² about the same axis. Initially both the
space probe and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 110 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the space probe's orientation by 24.0°?
(No Response) s
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Walking with a steady cadence is very important for covering long distances efficiently. How we place our feet, and how quickly we walk, also depends on the roughness of the surface we are walking upon and on the slope of the surface: we walk carefully on slippery surfaces, and take smaller steps when
hiking up a hill. When we are walking at constant speed in a fixed direction, the horizontal and vertical components of the acceleration of our center of mass must be zero. In addition, the sum of torques about the body's center of mass must also be zero. Consider the situation shown in the figure below.
ALMA
XCM
Х СМ
XCM XCM
XCM
We can model the walking gait of a person as a swing of the front leg and torso about the point where the front foot is planted (shown with a red circle in the figure) and a rotation of the trailing leg about the center of mass (CM) of the person. If each leg of this 78.0 kg person is 85.0 cm long and has a mass
of 13.8 kg, and 0; = 0₁ = 20.0°, what is the…
Chapter 10 Solutions
College Physics
Ch. 10 - Analogies exist between rotational and...Ch. 10 - Explain why centripetal acceleration changes the...Ch. 10 - In circular motion, a tangential acceleration can...Ch. 10 - Suppose a Piece of food is on the edge of a...Ch. 10 - The moment of inertia of a long rod spun around an...Ch. 10 - Why is the moment of inertia of a hoop that has a...Ch. 10 - Give an example in which anal forte exerts a large...Ch. 10 - While reducing the mass of a racing bike, the...Ch. 10 - A ball slides up a frictionless ramp. It is then...Ch. 10 - Describe the energy transformations involved when...
Ch. 10 - What energy transformations are involved when a...Ch. 10 - The Earth has more rotational kinetic energy now...Ch. 10 - When you start the engine of your car with the...Ch. 10 - Suppose a child walks from the outer edge of a...Ch. 10 - Suppose a child gets off a rotating...Ch. 10 - Helicopters have a small propeller on their tail...Ch. 10 - Whenever a helicopter has two sets of lifting...Ch. 10 - Describe how work is done by a skater pulling in...Ch. 10 - When there is a global heating trend on Earth, the...Ch. 10 - Nearly all conventional piston engines have...Ch. 10 - Jet turbines spin rapidly. They are designed to...Ch. 10 - An astronaut tightens a bolt on a satellite in...Ch. 10 - Competitive divers pull their limbs in and curl up...Ch. 10 - Draw a free body diagram to show how a diver gains...Ch. 10 - In terms of angular momentum, what is the...Ch. 10 - Describe different collisions—one in in which...Ch. 10 - Suppose an ice hockey puck strikes a hockey stick...Ch. 10 - While driving his motorcycle at highway speed, a...Ch. 10 - While driving his motorcycle at highway speed, a...Ch. 10 - Gyroscopes used in guidance systems to indicate...Ch. 10 - At its peak, a tornado is 60.0 m in diameter and...Ch. 10 - Integrated Concepts An ultracentrifuge accelerates...Ch. 10 - Integrated Concepts You have a grindstone (a disk)...Ch. 10 - Unreasonable Results You are told that a...Ch. 10 - With the aid of a string, a gyroscope is...Ch. 10 - Suppose a piece of dust finds itself on a CD. If...Ch. 10 - A gyroscope slows from an initial rate of 32.0...Ch. 10 - During a very quick stop, a car decelerates at...Ch. 10 - Everyday application: Suppose a yo-yo has a center...Ch. 10 - This problem considers additional aspects of...Ch. 10 - Calculate the moment of inertia of a skater given...Ch. 10 - The triceps muscle in the back of the upper arm...Ch. 10 - A soccer player extends her lower leg in a kicking...Ch. 10 - Suppose you exert a force of 180 N tangential to a...Ch. 10 - Consider the 12.0 kg motorcycle wheel shown in...Ch. 10 - Zorch, an archenemy of Superman, decides to slow...Ch. 10 - An automobile engine can produce 200 N m of...Ch. 10 - Starting with the formula for the moment of...Ch. 10 - Unreasonable Results A gymnast doing a forward...Ch. 10 - Unreasonable Results An advertisement claims that...Ch. 10 - This problem considers energy and work aspects of...Ch. 10 - What is the final velocity of a hoop that rolls...Ch. 10 - (a) Calculate the rotational kinetic energy of...Ch. 10 - Calculate the rotational kinetic energy in the...Ch. 10 - A baseball pitcher throws the ball in a motion...Ch. 10 - While punting a football, a kicker rotates his leg...Ch. 10 - A bus contains a 1500 kg flywheel (a disk that has...Ch. 10 - A ball with an initial velocity of 8.00 m/s rolls...Ch. 10 - While exercising in a fitness center, a man lies...Ch. 10 - To develop muscle tone, a woman lifts a 2.00-kg...Ch. 10 - Consider two cylinders that start down identical...Ch. 10 - What is the moment of inertia of an object that...Ch. 10 - Suppose a 200-kg motorcycle has two wheels like,...Ch. 10 - In softball, the pitcher throws with the arm fully...Ch. 10 - Construct Your Own Problem Consider the work done...Ch. 10 - (a) Calculate the angular momentum of the Earth in...Ch. 10 - (a) What is the angular momentum of the Moon in...Ch. 10 - Suppose you start an antique car by exerting a...Ch. 10 - A playground merry-go-round has a mass of 120 kg...Ch. 10 - Three children are riding on the edge of a...Ch. 10 - (a) Calculate the angular momentum of an ice...Ch. 10 - Consider the Earth-Moon system. Construct a...Ch. 10 - Repeat Example 10.15 in which the disk strikes and...Ch. 10 - Repeat Example 10.15 in which the disk originally...Ch. 10 - Twin skaters approach one another as shown in...Ch. 10 - Suppose a 0.250-kg ball is thrown at 15.0 m/s to a...Ch. 10 - Repeat Example 10.15 in which the stick is free to...Ch. 10 - Integrated Concepts The axis of Earth makes a...Ch. 10 - Prob. 1TPCh. 10 - Prob. 2TPCh. 10 - Prob. 3TPCh. 10 - Prob. 4TPCh. 10 - Prob. 5TPCh. 10 - Prob. 6TPCh. 10 - Prob. 7TPCh. 10 - Prob. 8TPCh. 10 - Prob. 9TPCh. 10 - Prob. 10TPCh. 10 - Prob. 11TPCh. 10 - Prob. 12TPCh. 10 - Prob. 13TPCh. 10 - Prob. 14TPCh. 10 - Prob. 15TPCh. 10 - Prob. 16TPCh. 10 - Prob. 17TPCh. 10 - Prob. 18TPCh. 10 - Prob. 19TPCh. 10 - Prob. 20TPCh. 10 - Prob. 21TPCh. 10 - Prob. 22TPCh. 10 - Prob. 23TPCh. 10 - Prob. 24TPCh. 10 - Prob. 25TPCh. 10 - Prob. 26TPCh. 10 - Prob. 27TPCh. 10 - Prob. 28TPCh. 10 - Prob. 29TPCh. 10 - Prob. 30TP
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- You are attending a county fair with your friend from your physics class. While walking around the fairgrounds, you discover a new game of skill. A thin rod of mass M = 0.550 kg and length l = 2.80 m hangs from a friction-free pivot at its upper end as shown in the figure. Pivot Velcro M Incoming Velcro-covered ball m The front surface of the rod is covered with Velcro. You are to throw a Velcro-covered ball of mass m = 1.20 kg at the rod in an attempt to make it swing backward and rotate all the way across the top. The ball must stick to the rod at all times after striking it. If you cause the rod to rotate over the top position (that is, rotate 180° opposite of its starting position), you win a stuffed animal. Your friend volunteers to try his luck. He feels that the most torque would be applied to the rod by striking it at its lowest end. While he prepares to aim at the lowest point on the rod, you calculate how fast he must throw the ball to win the stuffed animal with this…arrow_forwardA hanging weight, with a mass of m₁ = 0.365 kg, is attached by a rope to a block with mass m₂ = 0.835 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R₁ = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μ = 0.250. At the instant shown, the block is moving with a velocity of v; = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible. R₂ R₁ Mo mi (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. (No Response) m/s (b) What is the angular speed of the pulley (in rad/s) after the block has…arrow_forwardA stiff, thin, metal rod with negligible mass is free to rotate in a vertical plane about pivot point P, as shown in the figure below. The rod has three small beads (labeled 1, 2, and 3 in the figure), all with the same mass m, attached to it as shown. The rod is held horizontally and then released from rest at time t = 0. Find all results below in terms of the mass m, distance d, and acceleration due to gravity g. 1 P m m 2 2d 23 m 3 (a) What is the moment of inertia of the system of three particles about the pivot point P? I= (No Response) (b) What is the net torque magnitude about point P at t = 0? Tnet = (No Response) (c) What is the angular acceleration of the system about point P at t = 0? magnitude direction α = (No Response) (No Response) (d) What is the linear acceleration of bead 3 at t = 0? magnitude a = (No Response) direction (No Response) (e) What is the maximum kinetic energy of the system? K = (No Response) max (f) What is the maximum angular speed about point P…arrow_forward
- During a concentric loading of the quadriceps muscle in the upper leg, an athlete extends his lower leg from a vertical position (see figure (a)) to a fully extended horizontal position (see figure (b)) at a constant angular speed of 45.0° per second. Two of the four quadriceps muscles, the vastis intermedius and the rectus femoris, terminate at the patellar tendon which is attached to the top of the tibia in the lower leg. The distance from the point of attachment of the patellar tendon to the rotation axis of the tibia relative to the femur is 4.10 cm in this athlete. a b (a) The two quadriceps muscles can exert a maximum force of 225 N through the patellar tendon. This force is applied at an angle of 25.0° to the section of the tibia between the attachment point and the rotation axis. What is the torque (in N m) exerted by the muscle on the lower leg during this motion? (Enter the magnitude.) (No Response) N⚫ m (b) What is the power (in W) generated by the athlete during the motion?…arrow_forwardA 3.1-kg sphere is suspended by a cord that passes over a 1.6-kg pulley of radius 3.3 cm. The cord is attached to a spring whose force constant is k = 86 N/m as in the figure below. Assume the pulley is a solid disk. www m (a) If the sphere is released from rest with the spring unstretched, what distance does the sphere fall through before stopping? (No Response) m (b) Find the speed of the sphere after it has fallen 25 cm. (No Response) m/sarrow_forwardThe angular momentum vector of a precessing gyroscope sweeps out a cone as shown in the figure below. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by @p = t/L, where is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earth's axis of rotation precesses about the perpendicular to its orbital plane with a period of 2.58 × 104 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. (No Response) N⚫ marrow_forward
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- A war-wolf, or trebuchet, is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling pumpkins and pianos. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass 3.00 m long and joining particles of mass m₁ = 0.120 kg and m2 = 57.0 kg at its ends. It can turn on a frictionless horizontal axle perpendicular to the rod and 11.5 cm from the particle of larger mass. The rod is released from rest in a horizontal orientation. Find the maximum speed that the object of smaller mass attains when it leaves the trebuchet horizontally. (No Response) m/s m1 -3.00 m- m2arrow_forwardI just need help with part Barrow_forwardHow does torque differ from force?arrow_forward
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