ω F A 2 kg ball with radius 9 cm and radius of gyration of 7 cm is moving to the right at 2 m/s while a 5 N force is applied, accelerating its motion. It is currently backspinning (and therefore slipping) at w = 4 rad/s, with μk = 0.3. Find the acceleration of the balls center and also the angular acceleration of the ball at this instant a = m (positive right) $2 rad απ (positive $2 CCW)
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- The 300 kg cylinder shown in the figure is wrapped with rope as shown and released from rest. Find the angular acceleration and the distance travelled by the center of gravity in 3 seconds. rope cylinder. 1 m diameter A WA truck with 0.312 - m - radius tires travels at 28.2 m /s. What is the angular velocity of the rotating tires in radians per second?A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s²) of the centre of the disc is (correct to two decimal places). 100N
- Rod OA rotates counterclockwise at a constant angular rate 0-4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r= (1.6 cos 6) m. Both collars have a mass of 0.65 kg. Motion is in the vertical plane. (Figure 1) Figure r=1.6 cos 9. 0-4 rad/s 0.8 m 1 of 1 Part A Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant 0=45 Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) F= Value Submit μÁ Part B Previous Answers Units X Incorrect; Try Again; 5 attempts remaining Determine the magnitude of the force that OA exerts on the other colar at the instant @-45. Express your answer to three significant figures and include the appropriate units. View Available Hint(s)An automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular track2. A mass of 2 kg is placed on a bar at a distance of r = 1 m from the point 0. Initially, the bar is in a stationary state, as shown in the figure below. At t = 0, the bar starts a counter clockwise rotation around the point O at a constant angular acceleration of 1 rad/s?. It is known that the mass can stop on the bar without sliding until 0 = 30°. Based on these givens, please answer the following questions. a. What is the static friction coefficient between the mass and the bar? b. When the sliding starts, will the mass be moving towards the origin or away from the origin? 1 rad/s? 2 kg r = 1m
- What is the ang. velocity and acceleration of the disk when it rolls down the slope freely? Collar A slides downward along the vertical rod at a constant speed of 10 m/s, causing disk B to roll down the slope. Given raisk = 25 cm, AB = 1.5 m, and 40AB30°, determine using vector approach:: a) the absolute velocity of the disk, b) the absolute acceleration of the disk. = vdisk = -10.6287- 3.868j (m/s), a disk 123.0657 +44.7887j (m/s²)] B 20° loAs shown in the picture below, a 40-kg diver is positioned so that his radius of gyration is 0.4m as he leaves the board with an angular velocity of 5 rad/s (Position 1). What is the diver's angular velocity when he changes his pose to Position2, altering his radius of gyration to 0.2m? Position 1 Position 2 CARRod OA rotates counterclockwise at a constant angular rate 0 = 4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r = (1.6 cos 0) m. Both collars have a mass of 0.7 kg. Motion is in the vertical plane. (Figure 1) Figure r = 1.6 cos 0 0 = 4 rad/s 0.8 m 0 B < 1 of 1 A Part A Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant = 45° Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) F = 16.56 Submit Previous Answers Part B μA X Incorrect; Try Again; 5 attempts remaining FOA = Submit Determine the magnitude of the force that OA exerts on the other collar at the instant = 45°. Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) D N μA Value ? Units ?
- The sphere with mass m = 25 kg rolls down the inclined plane of angle = 25° without slipping. Determine its angular acceleration (in rad/s²). Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². 0.15 m Your Answer: G 0 Answer AA motorcycle cage has a curved path in the x-z plane as shown. The cage path has different curved profile, and between point o and A the path is best described as z = f(x) = ax², where a = 0.09 and b = 1.23. The motorcyclist at point M is moving at a velocity of 12.6 m/s which is increasing at a rate of 1.9 m/s?. If the horizontal position of the motorcyclist at point M is xM = 11.9 m, determine (i) the direction of the motorcyclisť's velocity. (ii) the radius of the curvature of the cage's path at point M, (iii) the normal acceleration at point M, (iv) the magnitude and direction of the motorcyclist's acceleration at point M. A (z = axBlocks A and B shown in the figure have masses of 5 kg and 10 kg respectively.If the pulley is treated as a 3 kg solid disk with a 15 cm radius, determine the acceleration of the block A. Disregard the rope mass and any slip on the pulley.Consider that the moment of inertia of the pulley is given by Ip = (1/2)mr² in which m is the mass of the pulley and r is of radius the pulley.