2. Consider the figure below; B 20 in. -y 30 in. 25 in. C a) Determine a unit vector en which acts in the direction of force F. b) Express F in Cartesian vector form, where F = 970 lb. c) Determine the moment of F about point O.

2. Consider the figure below; B 20 in. -y 30 in. 25 in. C a) Determine a unit vector en which acts in the direction of force F. b) Express F in Cartesian vector form, where F = 970 lb. c) Determine the moment of F about point O.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter10: Rotational Motion And Angular Momentum

Section: Chapter Questions

Problem 18CQ: Describe how work is done by a skater pulling in her arms during a spin. In particular, identify the...

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Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximately a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.
Competitive divers pull their limbs in and curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down (see below). Explain the effect of both actions on their angular velocities. Also explain the effect on their angular momentum.
Unreasonable Results A gymnast doing a forward flip lands on the mat and exerts a 500- Nm torque to slow and then reverse her angular velocity. Her initial angular velocity is 10.0 rad/s, and her moment of inertia is 0.050kgm2. (a) What time is required for her to exactly reverse her spin? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?
While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900kg-m2 the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0° with a constant force exerted by the muscle?
Describe how work is done by a skater pulling in her arms during a spin. In particular, identify the force she exerts on each arm to pull it in and the distance each moves, noting that a component of the force is in the direction moved. Why is angular momentum not increased by this action?
Eight children each of mass 40 kg, climb on a small merry-go-round. They position themselves evenly on the outer edge and join hands. The merry-go-round has a radius of 4.0 m and a moment of inertia 1000.0kgm2 . After the merry-go-round is given an angular velocity of 6.0 rev/min, the children walk inward and stop when they are 0.75 m from the axis of rotation. What is the new angular velocity of the merry-go-round? Assume there Is negligible frictional torque on the structure.
Suppose an ice hockey puck strikes a hockey stick that lies flat on the Ice and is free to move in any direction. Which quantities are likely to be conserved: angular momentum, linear momentum, or kinetic energy (assuming the puck and stick are very resilient)?
Explain how you might use the apparatus described in Figure OQ10.7 to determine the moment of inertia of the wheel. Note: If the wheel does not have a uniform mass density, the moment of inertia is not necessarily equal to 12 MR2.
The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min. (a) If the blades are 6000 kg each and the rotor assembly has three blades, calculate the angular momentum of the turbine at this rotation rate. (b) What Is the torque require to rotate the blades up to the maximum rotation rate in 5 minutes?
CHECK and THINK Our results give us a way to think about how a person might steer a unicycle. Consider the person, the unicycle, and the Earth as the system. No net torque acts on the system. Ignoring the motion of the Earth, Figure 13.37A shows the initial angular momentum of the system with the unicycle in motion: Li=Ltire. The person leans to his left so that the angular momentum of the tire rotates downward. The total angular momentum must still point to the right (Fig. 13.37B), so the angular momentum of the person must be upward to compensate. The persons angular velocity therefore points upward (parallel to his own angular momentum), and he is able to make a turn. Another way to analyze this situation is to exclude the Earth from the system and calculate the torque done by gravity. This approach is left as a homework problem. FIGURE 13.37 C Reanalyze the unicycles motion in Example 13.15 (page 382). This time, leave the Earth out of the system and explain how the torque exerted by gravity causes the unicycle to turn. Your explanation should involve a diagram.
Twin skaters approach one another as shown below and lock hands. (a) Calculate their final angular velocity given each had an initial speed of 2.50 m/s relative to the ice. Each has a mass of 70.0 kg and each has a center of mass located 0.800 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. (b) Compare the initial kinetic energy and final kinetic energy.
This problem considers energy and work aspects of Example 10.7—use data from that example as needed. (a) Calculate the rotational kinetic energy in the merry-go-round plus child when they have an angular velocity of 20.0 rpm. (b) Using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest. (c) Again, using energy considerations, calculate the force the father must exert to stop the merry-go- round in revolutions