A disk of mass m₂ = 70.0 g and radius r₁ = 4.50 cm slides on a frictionless sheet of ice with velocity v, where v = 12.00 m/s, as shown in a top-down view in figure (a) below. The edge of this disk just grazes the 1 edge of a second disk in a glancing blow. The second disk has a mass m₂ = 100 g, a radius r₂ = 5.00 cm, and is initially at rest. As the disks make contact, they stick together due to highly adhesive glue on the edge of each, and then rotate after the collision as shown in figure (b). m₂ a M₂ b Ⓡ (a) What is the magnitude of the angular momentum (in kg m²/s) of the two-disk system relative to its center of mass? kg-m²/s (b) What is the angular speed (in rad/s) about the center of mass? rad/s
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- A solid cylinder of mass m = 1kg, initially at rest, starts to roll down a rough surface inclined at a 300 angle to horizontal. The axis of the cylinder is attached through massless strings and pulleys to a square block of mass M = 2kg that rests initially on top of a horizontal table (see figure). What is the velocity of block M after the cylinder has traveled 1 m down the incline? The coefficient of kinetic friction between block M and the horizontal surface of the table is µ = 0.12. The cylinder rolls without slipping. M 0.37 m/s а. 2.50 m/s b. 1.62 m/s O c. 1.21 m/s O d. 1.43 m/s O e.A physical pendulum consists of a vertical board of of mass 6.52 kg, length 195 cm, and width 13 cm hanging from a horizontal, frictionless axle. A bullet of mass 147 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle. (a) If the bullet embedded itself in the board, what is the minimum speed the bullet could have to make this so? 37.41 m/s X (b) If the bullet passed through the board, reducing its speed by 1/5 its original value, what is the minimum speed of the bullet? 35.41 m/s X (c) If the bullet is made of rubber and rebounds elastically, what is the minimum speed the bullet could have? (d) What is the rebound speed of the bullet?The 29-1b rectangular plate is at rest on a smooth horizontal floor. It is given the horizontal impulses as shown in (Figure 1). Assume I = 20 lb. s. Figure 0.5 ft 5 lb.s 60% 2 ft -0.5 ft-- Part A Determine its angular velocity. Express your answer in radians per second to three significant figures. IVE ΑΣΦΑ ↓↑ vec w = 37.747 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part B Submit ***** Determine the magnitude of the velocity of the mass center. Express your answer in feet per second to three significant figures. VG = 22.2 ft/s Previous Answers ? rad/s
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