A very thin rigid plastic wheel of diameter D, consists of a rim and eight spokes, with a linear density of mass λ (for the rim and each spoke). The wheel is released from rest at the top of a slope of height h. Consider this wheel without slipping. (image 1) How fast does the center of mass of the wheel move when it reaches the base of the slope? answers (image 2)

A very thin rigid plastic wheel of diameter D, consists of a rim and eight spokes, with a linear density of mass λ (for the rim and each spoke). The wheel is released from rest at the top of a slope of height h. Consider this wheel without slipping. (image 1) How fast does the center of mass of the wheel move when it reaches the base of the slope? answers (image 2)

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Consider the frictionless marble-curve track system shown. Marble A is 100.0 g while marble B is 50.0 g. Suppose that both marbles are initially at rest. Right after collision, marble B has a velocity that is three times that of marble A. Ignore air resistance and rotational motion of the marbles. Furthermore, assume that the marbles are much smaller compared to the track.(a) Compute for the total initial mechanical energy associated with the two-marble system with respect to the bottom of the track.(b) Determine the final velocity of each marble after collision assuming that mechanical energy is conserved.(c) Give at least two reasons why in collision between two realistic bodies (that is, not perfectly rigid and with finite macroscopic size), contrary to the assumption in (b) above, mechanical energy is less likely to be conserved even if air resistance and friction can be neglected.
A diver (m = 60 kg) jumps from a diving board. At takeoff, his angular momentum about the transverse axis is 30 kg⋅m2/s. His radius of gyration about the transverse axis is 0.5 m at this instant. During the dive, he tucks and reduces his radius of gyrations about the transverse axis to 0.2 m. At takeoff, what is the diver’s moment of inertia about his transverse axis?
The Cavendish balance shown in the figure below has two large lead balls, each of mass M = 1.5 kg,and two smaller lead balls, each of mass m = 0.8 kg. The lengths of the suspended rod to which the twosmaller balls are attached and the fixed rod to which the larger balls are attached are both 40 cm asmeasured from the center of each lead ball. If the angle between the centers of the large and smallballs is  = 22 degrees with respect to the rotational axis established by the quartz fiber, find the force ofgravitational attraction between each pair of large and small balls.
In the figure, the driver of a car on a horizontal road makes an emergency stop by applying the brakes so that all four wheels lock and skid along the road. The coefficient of kinetic friction between tires and road is 0.49. The separation between the front and rear axles is L = 4.2 m, and the center of mass of the car is located at distance d = 1.9 m behind the front axle and distance h = 1.2 m above the road. The car weighs 12 kN. Find the magnitude of (a) the braking acceleration of the car, (b) the normal force on each rear wheel, (c) the normal force on each front wheel, (d) the braking force on each rear wheel, and (e) the braking force on each front wheel. (Hint: Although the car is not in translational equilibrium, it is in rotational equilibrium.) L.
Kathrine lets go of a cube of mass of m = 5 kilograms on her physics demo device she created. Her cube goes down a super smooth slide surface that has a height vertical distance of h=85 cm. At the end of the slide, her cube crashes into and sticks to the lower end of a vertical pole that has a mass M=10.5 kg and length 1-2.00m. Right after the crash, the pole pivots about a hinge point near its upper end through an angle (theta) before it stops for a moment. See the image given below to visualize Katherines system. You are tasked with Figuring out the following three things The speed of her cube just before it hits the pole The angular speed of the pole just after the crash The angle (theta) through which the pole pivots a. b. C. 0 Kathrine and her device
A uniform solid disk of mass m = 3.03 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.07 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? kg · m2/s Need Help? Read It
A 7 meter long stick is suspended from two strings. The stick has a mass of 17kg that is uniformily distributed. A 9kg dog is sitting 0.7m from the left end of the stick. Where is the center of mass? How do you know?
Among the elderly population, a sideway fall is a most frequent cause of hip fracture. An old man of mass 65 kg and height 1.7m was sent to Prince of Wales Hospital due to sideway fall. He slipped and fell laterally down with a straight body. Before falling, his centre of mass was 0.9 m above ground. His centre of mass was on the ground at the end of the fall. The radius of gyration about the anterior-posterior axis at his centre of mass was 0.55 m. (a) Calculate the initial potential energy before his fall. (b) Assuming his potential energy would be converted to linear kinetic energy of his centre of mass and rotational kinetic energy about his centre of mass, calculate the impact velocity v of his centre of mas right before he hit the ground. C. M. 1.7m 0.9m
The cylindrical plug A of mass mA = 2.7 kg is released from rest at B and slides down the smooth circular guide. The plug strikes the block C of mass mc = 2.1 kg and becomes embedded in it. Calculate the distances which the block and plug slide before coming to rest. The coefficient of kinetic friction between the block and the horizontal surface is uk = 0.38 and the distance r = 2.08 m. Hk Answer: s= i mc A MA B m
Before the collision, the cylinder was not rotating. What is the magnitude of its angular velocity after the collision? (units- rad/s)
Wind energy is gaining increased attention, generating an increased interest in windmill technology. Because windmill blades (vanes) rotate about a central axis, one of the most important physical properties of a windmill is its moment of inertia. Given is a picture of a typical windmill, where the geometry and center of mass of one of the vanes is illustrated. The mass of each vane is 411 kg. The distance from the center of mass of the vane to axis B is ?1=3.15 m. The distance from the center of mass of the vane to the center of the windmill hub is ��2=4.88 m. If the moment of inertia of a vane about axis A is 241 kg·m2 and about axis B is 5860 kg·m2, calculate the moment of inertia ?total of the entire assembly about the axis that passes through the windmill's hub and is perpendicular to the screen. (Ignore the hub and assume the vanes are flat.)
Two identical tops, #1 and #2, spin with angular velocities ω1 = 10 rad/s counterclockwise and ω2 = 12 rad/s clockwise. The tops bump into one another and separate. After the collision, the first top has angular velocity of 5 rad/s counterclockwise. During the collision, the force of impact is along the line connecting the centers of the top, so no torque is exerted on either top. What is the magnitude of the angular velocity of the second top? Does the top spin clockwise or counterclockwise?