A horizontal merry-go-round is initially at rest. At t = 0, it is given a constant angular acceleration ? = 0.0710 rad/s2, which increases its angular velocity. A 23.5 kg child sits at 2.35 m from the axis of rotation.   (a) At t = 9.70 s, determine the centripetal force acting on the child. ________  N   (b) At t = 9.70 s, determine the direction of the net force acting on the child. Specify the angle from the radially inward direction.  ________ °   (c) Through how many radians has the merry-go-round rotated within that 9.70 s time?   _______ rad

Q: A 1.25 g pepperoni rests at a distance of 7.5 cm from the centre of a pizza being spun by the pizza…

A: mass (m) = 1.25 g = 0.00125 kg distance from center (r) = 7.5 cm = 0.075 m Angular speed (ω) = 68…

Q: You have a grindstone (a solid disk) that is 642.93 kg, has a 0.114-m radius, and is turning at…

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Q: takeoff a commercial jet has a 70.0 m/s speed. Its tires have a diameter of 0.400 m.(a) At how many…

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Q: An athlete swings a 3.40-kg ball horizontally on the end of a rope. The ball moves in a circle of…

A: Given that:m=3.40 kgr=0.600 mω=0.650 rev/s

Q: You want to centrifuge at 2660 g and the centrifuge has a radius of rotation of 9.5 cm. What RPM…

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Q: It has been suggested that rotating cylinders about 11.0 mi long and 5.92 mi in diameter be placed…

A: Given: Length of cylinder, L=11 mi = 17702.784 m Diameter of cylinder, d=5.92 mi = 9527.316 m     To…

Q: At takeoff a commercial jet has a 70.0 m/s speed. Its tires have a diameter of 0.400 m. (a) At how…

A: Linear speed of commercial jet (v) = 70 msdiameter of tires (d) = 0.400 m radius of tires (r) =…

Q: Part (f) Finally, the boy decides that he has had enough fun. He decides to crawl to the outer edge…

A: Given R = 1.3 m M = 241 kg m = 46 kg v =1.8 m/s

Q: You have a grindstone (a disk) that is 198.641 kg, has a 0.699-m radius, and is turning at 97.425…

A: Givenmass of the grinstone M=198.641 kgradius of the grindstone R=0.699 minitial angular speed…

Q: It has been suggested that rotating cylinders about 17.5 mi long and 6.12 mi in diameter be placed…

A:

Q: A pendulum is 0.280 m long, and the bob has a mass of 1.00 kg. At the bottom of its swing, the bob's…

A: A pendulum swing can be considered as a small part of vertical rotation. Therefore, other than…

Q: An athlete swings a 5.30-kg ball horizontally on the end of a rope. The ball moves in a circle of…

A: Mass of ball (m) = 5.30 kg radius of circle (r) = 0.950 m angular speed (ω) = 0.410 rev/sec

Q: fixed axis 0.69 m away. The mass is initially at rest and undergoes a constant angular acceleration…

A: Given: The Mass(m)= 0.39 kg. The distance (R)= 0.69 m. The angular acceleration α=4.77 rad/s2 The…

Q: being spun in a vertical Circie Wi niform spEed v=4 fm/S. (a) What is the tangential (parallel to v…

A: As it is given in the question that uniform speed of 4m/s.  So, dv/dt = 0 Ans: 0 m/s2

Q: A child sits on a merry‑go‑round that has a diameter of 4.00 m. The child uses her legs to push the…

A: Given: Diameter (d) = 4 m               Angular speed (wf) = 16 rpm                 time (t) = 42…

Q: The car A has a forward speed of 19 km/h and is accelerating at 3.7 m/s². Determine the velocity and…

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Q: Zorch, an archenemy of Superman, decides to slow the Earth's rotation to once per 28.0 hours by…

A: initial angular velocity of earth,ω0=2π23×60×60+(56×60)+(4)s=72.92×10-6 rad/sFinal angular velocity…

Q: (a) A 15.0 kg child is riding a playground merry-go-round that is rotating at 30.0 rev/min. What…

A: Centripetal force -  Centripetal force is defined as the force in which the force makes a body…

Q: It has been suggested that rotating cylinders about 17.0 mi long and 4.55 mi in diameter be placed…

A:

Q: A wind turbine is rotating counterclockwise at 0.78 rev/s and slows to a stop in 17 s. Its blades…

A: As per our guidelines, we are supposed to answer only first three subparts in case of multiple…

Q: The County Fair Swing carries the mass of riders and chairs in an unchanging circular path in an…

A: Since the ride is moving in horizontal direction, its acceleration in vertical direction and hence…

Q: A point mass of 0.44 kg is set to rotate about a fixed axis 0.81 m away. The mass is initially at…

A: The centripetal force is given by F=v2r Here, v is the speed and r is the distance of the point mass…

Q: The coordinate axes shown represent the principal centroidal axes of inertia of a 3000-lb space…

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Q: A child stands on a playground merry-go-round a distance of 1.50m from the rotation axis. The…

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Q: 1. A block of mass M-10 kg is connected to another block of mass m=5 kg via cylindrical pully of…

A: Draw the free body diagram of the system and then apply the Newton's second law of motion for the…

Q: It has been suggested that rotating cylinders about 20.0 mi long and 5.69 mi in diameter be placed…

A:

Q: The car A has a forward speed of 17 km/h and is accelerating at 3.5 m/s². Determine the velocity and…

A: Given: vA=17km/h = 4.72 m/saA=3.5 m/s2r=7.8 mΩ=2.5 rev/min=0.262 rad/sθ=41°

Q: A horizontal merry-go-round is initially at rest. At t= 0, it is given a constant angular…

A: a) Apply the first angular kinematic equation and substitute the required values to calculate the…

Q: If we assume that the tip of the mandible hits perpendicular to ground, what is the force on the…

A: Given : length, l = 1.30 mm = 1.3 × 10-3 m Mass, m = 130×10-6 g = 1.30 × 10-7 kg Angular…

Q: The car A has a forward speed of 17 km/h and is accelerating at 3.5 m/s?. Determine the velocity and…

A:

Q: In an amusement park rocket ride, cars are suspended from 4.25-m cables attached to the rotating…

A: According to Newton's 2nd Law in X-direction:∑Fx=Tsinθ=marTsinθ=mar------(1)we know,…

Q: If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the…

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Q: Plot (Graph) the Centripetal Force as a function of Angular Velocity Static Force  Angular Velocity…

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Q: One end of a cord is fixed and a small 0.550-kg object is attached to the other end, where it swings…

A: Given: Mass of object, m = 0.55 kg Radius, r = 1.5 m Angle, = 17 degree Speed of object, v = 6 m/s

Q: A 50.0-kg child stands at the rim of a merry-go-round of radius 2.85 m, rotating with an angular…

A: mass of child = 50 kg Radius = 2.85 m w ( angular speed) = 3.9 rad/sec

Q: A .38 kg mass tied to the end of a 0.3m long string is pulled in a circle by If it is moving with an…

A: Given:-  Mass m= 0.38 kg  The length of the string L = 0.3 m  The angular speed ω= 9.3 rad/sec…

Q: A large centrifuge is used to expose aspiring astronauts to accelerations similar to those…

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Q: How many revolutions per minute would a 30 m -diameter Ferris wheel need to make for the passengers…

A: d=30 mr=15 mThe passenger is weightless at the top.

Q: It has been suggested that rotating cylinders about 15.0 mi long and 5.89 mi in diameter be placed…

A: Given, l= 15mi =15*1609m = 24135 m d= 5.89mi = 5.89*1609m =9477.01 m Where, l is the length of the…

Q: It has been suggested that rotating cylinders about 13.0 mi long and 4.81 mi in diameter be placed…

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Q: The force is F=3j+Sk (N) acts at the position r=2i from the axis of rotation. Determine the torque…

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Q: It has been suggested that rotating cylinders about 18.5 mi long and 4.60 mi in diameter be placed…

A:

Q: A goat stands on a merry-go-round that is rotating at 6.1 rad/s. If the coefficient of static…

A: Given Angular speed of the merry-go-round is ω=6.1 rad/s Coefficient of static friction between the…

Q: A 50.0-kg child stands at the rim of a merry-go-round of radius 2.90 m, rotating with an angular…

A: Given :           mass m = 50 kg           radius r = 2.90       angular speed ω= 3.65 rad/si…

Q: A 15.0 kg child is riding a playground merry-go-round that is rotating at 50.0 rev/min. What…

A: Given that :Mass of the child 'm'=15 kgRotational speed N=50 rev/minShe is 1.50 m from its center

Q: A point mass of 0.36 kg is set to rotate about a fixed axis 0.72 m away. The mass is initially at…

A: The angular final velocity is,

Q: You have a horizontal grindstone (a disk) that is 95 kg, has a 0.36 m radius, is turning at 86 rpm…

A: The torque due to the frictional force is τ=r×f  =rμN…

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.