Calculate the linear momentum (L) of a motor car whieel which has a radius of gyration (kG) = 550 mm. diameter 1.0m and mass = 7.5 kg. The wheel is moving at an angular velocity, @=3.5 rad's.
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- A uniform crate C with mass m is being transported to the left by a forklift with a constant speed v1 . What is the magnitude of the angular momentum of the crate about point D , that is, the upper left corner of the crate?a. 0b. mv 1ac. mv 1 bd. mv 1Given the following diagram: 1) Indicate/Sketch the LOI (line of impact) 2) Indicate what component of momentum is conserved (Choices stated below) a) Horizontal Component Only b) Vertical Component Only c) Component of the momentum of the ball along a perpendicular axis relative to inclined surface d) Component of the momentum of the ball along a parallel axis relative to inclined surfaceAngular Momentum of a Particle Two identical spheres with m=3 kg each are rigidly attached to the rotating light rigid structure. The velocity of the spheres is v=2 m/s. Determine the angular momentum about the axis of rotation.
- Given the following diagram: 1) Indicate/Sketch the LOI (line of impact) 2) What component of momentum is conserved from the following choices (Choose only one) a) Horizontal Component Only b) Vertical Component Only c) Component of the momentum of the ball along a perpendicular axis relative to inclined surface d) Component of the momentum of the ball along a parallel axis relative to inclined surfaceA uniform crate C with mass m is being transported to the left by a forklift with a constant speed v1 . What is the magnitude of the angular momentum of the crate about point A , that is, the upper left corner of the crate?a. 0b. mv 1dc. 3mv1d. mv 1Asubject of mass 65 kg has her gait analyzed. Suppose that the x componentof the force measured by a force plate takes the shape shown in Fig. (a) If the forward velocity of the walker is 2 m/s at heel strike, what is it0.4 s after heel strike?(b) Estimate the corresponding change in height for the subject’s center ofgravity (i.e., from heel strike to 0.4 s later).
- Consider a slender rod AB with a length l and a mass m. The ends are connected to blocks of negligible mass sliding along horizontal and vertical tracks. If the rod is released with no initial velocity from a horizontal position as shown in Fig.A, determine its angular velocity after it has rotated through an angle of θ (see Fig B) using the conservation of energy method. (Hint: Moment of inertia of rod about G = (1/12)ml2 The kinetic energy of a rigid body in plane motion isA 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.A particle M1, weighing 2.4 Ibs, is tied to a thread and describes a circular path in a horizontal plane. The thread, of negligible mass, passes through a hole in the center of the circle and descends vertically. Another particle M2 is attached, weighing 5.0 Ibs, as shown in the figure. If M1 describes a uniform circular motion, with angular velocity w 3.1 rad/s, determine the radius R of the circumference in inches.
- Bicycle wheels are manufactured having thin rims and tires of total mass D per unit length, and the spokes and axle may be ignored. Find the angular momentum of one bicycle wheel of radius r when the bicycle is traveling at velocity v, and hence comment upon whether you would prefer large wheels or small wheels to make a bicycle easiest to balance when riding it.5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to 3.1415 rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his…Define moment of momentum.