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: An athlete swings a 6.00-kg ball horizontally on the end of a rope. The ball moves in a circle of…

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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: A 80 Kg man rides a spinning amusement park ride that has a radius of 10.8 m. If the person's…

A: Given data :              Mass of the man , m = 80 kg              Radius , r = 10.8m…

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

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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: It has been suggested that rotating cylinders about 16.5 mi long and 4.65 mi in diameter be placed…

A: Given data The length of the cylinder is l = 16.5 mi. The diameter of the cylinder is d = 4.65 mi =…

Q: An athlete swings a 6.90-kg ball horizontally on the end of a rope. The ball moves in a circle of…

A: Given: The mass of the ball is 6.9 kg. The radius of the circular path is 0.67 m. The angular speed…

Q: It has been suggested that rotating cylinders about 20.0 mi long and 3.53 mi in diameter be placed…

A: It is given that, l=20 mi=32186.9 md=3.53 mir=d2=3.532=1.765 mi=2840.4922 m

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…

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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 goat stands on a merry-go-round that is rotating at 5.3 rad/s. If the coefficient of static…

A: Given data The angular speed of the merry-go-round is given as ω=5.3 rad/s. The coefficient of…

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: A 50.0 kg child stands at the rim of a merry-go-round of radius 2.20 m, rotating with an angular…

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

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Q: It has been suggested that rotating cylinders about 17.5 mi long and 6.31 mi in diameter be placed…

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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: 1. A car is driven along a circular path with radius 10 km. If it runs 3 times around the path for…

A: As per our guidelines we will solve first three part for you. To get remaining part solved please…

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 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: A wind turbine is rotating counterclockwise at 0.78 rev/s and slows to a stop in 21 s. Its blades…

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Q: A laboratory centrifuge like the one shown in the figure operates with a rotational speed of 12000…

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Q: A 80 Kg man rides a spinning amusement park ride that has a radius of 10.8 m. If the person's…

A: Given:- Mass of the man is m=80 Kg Radius of the ride R=10.8 m Tangential speed of the man is v=12.7…

Q: A 50.0-kg child stands at the rim of a merry-go-round of radius 2.95 m, rotating with an angular…

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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: A 100 kg vehicle enters a flat circular turn of radius 5 m. It is initially traveling at 5 m/s…

A: Given data: The mass of vehicle is m=100 kg. The radius of circle is r=5 m. The initial speed is…

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

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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: 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…

Q: It has been suggested that rotating cylinders about 11.0 mi long and 3.63 mi in diameter be placed…

A: The length of a cylinder is, L=11 mi=11 mi×1609.34 m1 mi=17702.74 m The radius of a cylinder is,…

Q: It has been suggested that rotating cylinders about 11.5 mi long and 4.18 mi in diameter be placed…

A: Diameter = 2 r = 4.18 mi = 6727.058 m free fall acceleration on earth = a = 9.8 m/s2

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.