09:49Physics - Mechanics: Application of Moment of Inertia and Angular Acceleration (2 of 2)Michel van Biezen464views
Multiple ChoiceSuppose that piano has a long, thin bar ran through it (totally random), shown below as the vertical red line, so that it is free to rotate about a vertical axis through the bar. You push the piano with a horizontal 100 N (blue arrow), causing it to spin about its vertical axis with 0.3 rad/s2 . Your force acts at a distance of 1.1 m from the bar, and is perpendicular to a line connecting it to the bar (green dotted line). What is the piano's moment of inertia about its vertical axis?774views3rank2comments
Multiple ChoiceA 400g particle is moving in circular motion with a radius of 2.3m. At one instant in time its speed was 3.4m/s and it was slowing down at a rate of 2.2m/s2. What was the magnitude of the net force on the particle at this instant?333views
Multiple ChoiceA hollow sphere with a radius of 0.31 m is placed on an inclined plane that makes an 11° angle with the floor. Assuming the sphere rolls without slipping, what will be the magnitude of the acceleration of the sphere down in the incline?495views
Textbook QuestionA cord is wrapped around the rim of a solid uniform wheel 0.250 m in radius and of mass 9.20 kg. A steady horizontal pull of 40.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. (b) Find the magnitude and direction of the force that the axle exerts on the wheel. 2347views2rank
Textbook QuestionA 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley (Fig. E10.16). The pulley has the shape of a uniform solid disk of mass 2.00 kg and diameter 0.500 m. After the system is released, find (b) the acceleration of the box, and4718views
Textbook QuestionCP A 15.0-kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 12.0 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 10.0 m to the water. (b) With what speed does the bucket strike the water?1464views
Textbook QuestionCP A 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m, to a hanging book with mass 3.00 kg. The system is released from rest, and the books are observed to move 1.20 m in 0.800 s. (a) What is the tension in each part of the cord?1146views2rank
Textbook QuestionA machine part has the shape of a solid uniform sphere of mass 225 g and diameter 3.00 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. (a) Find its angular acceleration.626views
Textbook QuestionA playground merry-go-round has radius 2.40 m and moment of inertia 2100 kg•m^2 about a vertical axle through its center, and it turns with negligible friction. A child applies an 18.0-N force tangentially to the edge of the merry-go-round for 15.0 s. If the merry-go-round is initially at rest (b) How much work did the child do on the merry-go-round?777views
Textbook QuestionCP A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in Fig. 10.10. The pulley is a uniform disk with mass 10.0 kg and radius 30.0 cm and turns on frictionless bearings. You measure that the stone travels 12.6 m in the first 3.00 s starting from rest. Find (b) the tension in the wire.2766views1rank1comments
Textbook QuestionThe flywheel of an engine has moment of inertia 1.60 kg/m^2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8.00 s, starting from rest?652views1rank
Textbook Question(II) A softball player swings a bat, accelerating it from rest to 2.4 rev/s in a time of 0.20 s. Approximate the bat as a 0.90-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.119views
Textbook QuestionA large spool of rope rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance ℓ, holding onto it, Fig. 10–70. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?<IMAGE>171views
Textbook QuestionA 12-cm-diameter, 600 g cylinder, initially at rest, rotates on an axle along its axis. A steady 0.50 N force applied tangent to the edge of the cylinder causes the cylinder to reach an angular velocity of 500 rpm in 2.0 s. What is the magnitude of the frictional torque between the cylinder and the axle?950views
Textbook QuestionYour engineering team has been assigned the task of measuring the properties of a new jet-engine turbine. You've previously determined that the turbine's moment of inertia is 2.6 kg m^2. The next job is to measure the frictional torque of the bearings. Your plan is to run the turbine up to a predetermined rotation speed, cut the power, and time how long it takes the turbine to reduce its rotation speed by 50%. Your data are given in the table. Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the frictional torque. 152viewsTextbook QuestionA 30-cm-diameter, 1.2 kg solid turntable rotates on a 1.2-cm-diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 15 seconds. How much friction force does the brake pad apply to the shaft?270viewsTextbook QuestionA hollow cylinder (hoop) is rolling on a horizontal surface at speed v = 3.0 m/s when it reaches an 18° incline.(a) How far up the incline will it go?131viewsTextbook QuestionA 1.6-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of 22 rev/s from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.204viewsTextbook QuestionSuppose David puts a 0.60-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle, accelerating it from rest to a rate of 75 rpm after 4.5 s. What is the torque required to achieve this feat, and where does the torque come from?152viewsTextbook Question(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate(a) the torque needed,<IMAGE>131viewsTextbook Question(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm<IMAGE>179viewsTextbook Question(II) A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to(a) the car and ?139viewsTextbook Question(II) A rotating uniform cylindrical platform of mass 220 kg and radius 5.5 m slows down from 3.8 rev/s to rest in 18 s when the driving motor is disconnected. Estimate the power output of the motor (hp) required to maintain a steady speed of 3.8 rev/s .140viewsTextbook QuestionWater drives a waterwheel (or turbine) of radius R = 3.0 m as shown in Fig. 11–50. The water enters at a speed v₁ = 7.0m/s and exits from the waterwheel at a speed v₂= 3.8 m/s.(c) If the water causes the waterwheel to make one revolution every 6.0 s, how much power is delivered to the wheel?<IMAGE>129viewsTextbook QuestionIf a billiard ball is hit in just the right way by a cue stick, the ball will roll without slipping immediately after losing contact with the stick. Consider a billiard ball (radius r, mass M) at rest on a horizontal pool table. A cue stick exerts a constant horizontal force F on the ball for a time t at a point that is a height h above the table’s surface (see Fig. 10–78). Assume that the coefficient of static friction between the ball and table is μₛ . Determine the value for h so that the ball will roll without slipping immediately after losing contact with the stick.<IMAGE>167viewsTextbook Question"A boy rolls a tire along a straight level street. The tire has mass 8.0 kg, radius 0.32 m and moment of inertia about its central axis of symmetry of 0.83 kg·m². The boy pushes the tire forward away from him at a speed of 2.1 m/s and sees that the tire leans 12° to the right (Fig. 11–49). (a) How will the resultant torque due to gravity and the normal force F→_N affect the subsequent motion of the tire? <IMAGE>"131viewsTextbook Question(II) Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 10–57. The ball is accelerated uniformly from rest to 8.5 m/s in 0.38 s, at which point it is released. Calculate(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at its end.<IMAGE>123viewsTextbook QuestionA particle of mass m uniformly accelerates as it moves counterclockwise along the circumference of a circle of radius R: r→ = î R cos θ + ĵ R sin θwith θ = ω₀t + (1/2)αt² , where the constants ω₀ and α are the initial angular velocity and angular acceleration, respectively. Determine the object’s tangential acceleration a→_tan and determine the torque acting on the object using (b) τ→ = Iα→ .217viewsTextbook Question(II) To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 10–61. Suppose that the satellite has a mass of 3600 kg and a radius of 4.0 m, and that the rockets each add a mass of 250 kg. What is the steady force required of each rocket if the satellite is to reach 28 rpm in 5.0 min, starting from rest?<IMAGE>192viewsTextbook Question(II) A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to(b) the ground?116viewsTextbook Question(II) Calculate the moment of inertia of the array of point objects shown in Fig. 10–58 about the y axis, and the x axis. Assume m = 22kg, M = 3.2kg, and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the x axis.(c) About which axis would it be harder to accelerate this array?<IMAGE>149viewsTextbook Question(II) A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 330 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge? 160viewsTextbook QuestionA solid ball is released from rest and slides down a hillside that slopes downward at 65.0° from the horizontal. (c) In part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?103viewsTextbook QuestionA solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. Figure 10–76 shows a view from above. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. When the cm has moved a distance of 5.2 m, determine(c) how fast the disk is spinning (in radians per second.<IMAGE>97viewsTextbook Question(II) A potter is shaping a bowl on a potter’s wheel rotating at constant angular velocity of 1.6 rev/s (Fig. 10–59). The friction force between her hands and the clay is 1.8 N total.(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hands? The moment of inertia of the wheel and the bowl is 0.11 kg • m².<IMAGE>94viewsTextbook Question(II) A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.380 kg. Calculate(b) the applied torque needed to accelerate it from rest to 1950 rpm in 5.00 s. Take into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 55.0 s.95viewsShowing 36 of 36 practiceMore practice (0)
Textbook QuestionA 30-cm-diameter, 1.2 kg solid turntable rotates on a 1.2-cm-diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 15 seconds. How much friction force does the brake pad apply to the shaft?270views
Textbook QuestionA hollow cylinder (hoop) is rolling on a horizontal surface at speed v = 3.0 m/s when it reaches an 18° incline.(a) How far up the incline will it go?131views
Textbook QuestionA 1.6-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of 22 rev/s from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.204views
Textbook QuestionSuppose David puts a 0.60-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle, accelerating it from rest to a rate of 75 rpm after 4.5 s. What is the torque required to achieve this feat, and where does the torque come from?152views
Textbook Question(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate(a) the torque needed,<IMAGE>131views
Textbook Question(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm<IMAGE>179views
Textbook Question(II) A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to(a) the car and ?139views
Textbook Question(II) A rotating uniform cylindrical platform of mass 220 kg and radius 5.5 m slows down from 3.8 rev/s to rest in 18 s when the driving motor is disconnected. Estimate the power output of the motor (hp) required to maintain a steady speed of 3.8 rev/s .140views
Textbook QuestionWater drives a waterwheel (or turbine) of radius R = 3.0 m as shown in Fig. 11–50. The water enters at a speed v₁ = 7.0m/s and exits from the waterwheel at a speed v₂= 3.8 m/s.(c) If the water causes the waterwheel to make one revolution every 6.0 s, how much power is delivered to the wheel?<IMAGE>129views
Textbook QuestionIf a billiard ball is hit in just the right way by a cue stick, the ball will roll without slipping immediately after losing contact with the stick. Consider a billiard ball (radius r, mass M) at rest on a horizontal pool table. A cue stick exerts a constant horizontal force F on the ball for a time t at a point that is a height h above the table’s surface (see Fig. 10–78). Assume that the coefficient of static friction between the ball and table is μₛ . Determine the value for h so that the ball will roll without slipping immediately after losing contact with the stick.<IMAGE>167views
Textbook Question"A boy rolls a tire along a straight level street. The tire has mass 8.0 kg, radius 0.32 m and moment of inertia about its central axis of symmetry of 0.83 kg·m². The boy pushes the tire forward away from him at a speed of 2.1 m/s and sees that the tire leans 12° to the right (Fig. 11–49). (a) How will the resultant torque due to gravity and the normal force F→_N affect the subsequent motion of the tire? <IMAGE>"131views
Textbook Question(II) Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 10–57. The ball is accelerated uniformly from rest to 8.5 m/s in 0.38 s, at which point it is released. Calculate(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at its end.<IMAGE>123views
Textbook QuestionA particle of mass m uniformly accelerates as it moves counterclockwise along the circumference of a circle of radius R: r→ = î R cos θ + ĵ R sin θwith θ = ω₀t + (1/2)αt² , where the constants ω₀ and α are the initial angular velocity and angular acceleration, respectively. Determine the object’s tangential acceleration a→_tan and determine the torque acting on the object using (b) τ→ = Iα→ .217views
Textbook Question(II) To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 10–61. Suppose that the satellite has a mass of 3600 kg and a radius of 4.0 m, and that the rockets each add a mass of 250 kg. What is the steady force required of each rocket if the satellite is to reach 28 rpm in 5.0 min, starting from rest?<IMAGE>192views
Textbook Question(II) A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to(b) the ground?116views
Textbook Question(II) Calculate the moment of inertia of the array of point objects shown in Fig. 10–58 about the y axis, and the x axis. Assume m = 22kg, M = 3.2kg, and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the x axis.(c) About which axis would it be harder to accelerate this array?<IMAGE>149views
Textbook Question(II) A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 330 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge? 160views
Textbook QuestionA solid ball is released from rest and slides down a hillside that slopes downward at 65.0° from the horizontal. (c) In part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?103views
Textbook QuestionA solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. Figure 10–76 shows a view from above. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. When the cm has moved a distance of 5.2 m, determine(c) how fast the disk is spinning (in radians per second.<IMAGE>97views
Textbook Question(II) A potter is shaping a bowl on a potter’s wheel rotating at constant angular velocity of 1.6 rev/s (Fig. 10–59). The friction force between her hands and the clay is 1.8 N total.(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hands? The moment of inertia of the wheel and the bowl is 0.11 kg • m².<IMAGE>94views
Textbook Question(II) A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.380 kg. Calculate(b) the applied torque needed to accelerate it from rest to 1950 rpm in 5.00 s. Take into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 55.0 s.95views
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