5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height?

5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

bucket of mass m is hanging from the free end of a rope whose other end is wrapped around a drum (radius R, mass M) that can rotate with negligible friction about a stationary horizontal axis. The drum is not a uniform cylinder and has unknown moment of inertia. When you release the bucket from rest, you find that it has a downward acceleration of magnitude a. What are (a) the tension in the cable between the drum and the bucket and (b) the moment of inertia of the drum about its rotation axis?
3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.
A min cage of mass 4t is to be raised with an acceleration of 1.5m/s2 by a cable passing over a hoist drum of 1.5m diameter. What is the power required when the load has reached a velocity of 6m/s, neglecting the inertia of the drum and weight of the cable, but allowing for bearing friction torque of 3kN at the drum? What is the power required at a uniform velocity of 6m/s
A spool of mass 60 kg is supported on two rollers at A and B as shown in Figure Q1(c). Neglect the mass of the inelastic cable, friction and the mass of the rollers at A and B. Knowing that a constant pulling force P is applied in order to unwind 6 m of cable in 3 s starting from rest. The radius of gyration for the spool is (600+a) mm, where a = 8. Appendix A shows the examples of identifying the radius of gyration using student ID. Determine the pulling force P.
A spool of mass 60 kg is supported on two rollers at A and B as shown in FigureQ1(c). Neglect the mass of the inelastic cable, friction and the mass of therollers at A and B. Knowing that a constant pulling force P is applied in order tounwind 6 m of cable in 3 s starting from rest. The radius of gyration for the spoolis (604) mm, Appendix Ashows the examples of identifying the radius of gyration using student ID.(i) Determine the angular acceleration of the spool. (ii) Determine the pulling force P. (iii) Explain with calculation on ways to increase the acceleration of cablebeing pulled. [
A barrel of asphalt weighing 450 N starts from rest at Aand rolls without friction along a vertical parabolic curveACB with dimensions L = 6.00 m and d = 1.20 m. Find thenormal force between the barrel and the path at the lowestpoint C. Hint: You need to determine the radius of thecurvature at point C.
A motorcycle and rider have a combined mass of 350kg. The each wheel has a mass of 20kg with the diameter of 500 mm. The rider accelerates from 5m/s to 25m/s over a distance of 100m, whilst climbing a hill of slope 1 in 20. Identify the magnitude and effect of gyroscopic reaction torque by calculating the angular velocity and power as the motorcycle ascends the incline when the motorcycle and rider travel at 80 km/h around a left-hand bend of road with the radius 30 m.Explain the effects of energy transfer in mechanical systems (e.g. gears, pulley or flywheel) with uniform acceleration present.
In your job as a mechanical engineer you are designing aflywheel and clutch-plate system. DiskA is made of a lighter material than disk B, and the moment of inertia ofdisk A about the shaft is one-third that of disk B. The moment ofinertia of the shaft is negligible. With the clutch disconnected, A isbrought up to an angular speed v0; B is initially at rest. The acceleratingtorque is then removed from A, and A is coupled to B. (Ignorebearing friction.) The design specifications allow for a maximum of2400 J of thermal energy to be developed when the connection ismade. What can be the maximum value of the original kinetic energyof disk A so as not to exceedthe maximum allowed value of the thermalenergy?
The small end rollers of the 8-lb uniform slender bar (length = 4 ft) are constrained to move in the slots, which lie in the verticalplane. At the instant when θ = 30°, the velocity of roller A is 14 ft/s down the vertical slot. Determine the angular acceleration of the bar, the acceleration of mass center G, and the reactions of points A and B, under the action of the 6-lb force P. Neglect the friction and the mass of the small rollers.
A weight with mass mw=150 g is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R=4.00 cm and mass Ms=200 g. Find the magnitude ?a of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. Use ?=9.81 m/s2. Find the tension T in the thread.
A 256-lb block is released from rest when the spring is unstretched. The drum has a weight of 76 lb and a radius of gyration of kO = 0.9 ft about its center of mass O. The coefficient of stiffness of the spring is k=78 lb/ft. The radius of the drum are: rin=0.485ft and rout=0.82ft. Find the velocity of the block after it has descended d=4 feet.
The 2.00-kg slender rod shown is hanging in a vertical position and is pin-supported at point A. The slender rod is initially at rest until a 1.000-kg block C, strikes it at its end at point B.The block slides on a frictionless surface with a velocity of 3.50 m/s to the right. After the impact, it slides with a velocity of 1.250 m/s to the right, and the bar rotates with an angular velocity, ω'. 1. What gives the correct kinematic relationship relating the final velocity of the center of the rod, v' , and its angular velocity, ω'? 2. What is the coefficient of restitution, e, between the block and the slender rod? 3. What is the magnitude of the horizontal impulse at the support at point A?