A disk with a mass of "m" kg and radius of "r" meters (l =1/2mr^2) rolls without slipping at "v" m/s. 1. What is its total kinetic energy (in terms of m,r, and v)?

Q: Two bugs, Buzz and Crunchy, are siting on a spinning disk. Buzz is sitting halfway and Crunchy is…

A: Radius of the disk r=1.4 m and angular speed of the disk about its center w=41 rpm=41/60 rps. We…

Q: An 7.00-cm-diameter, 370 g hollow sphere is released from rest at the top of a 1.90-m-long, 20.0*…

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Q: Ex. 46: A flywheel in the form of a disc of mass 10 kg and radius 50 cm is rotating with a constant…

A: To find - Angular momentum (L)=? Rotational K.E.=? Given- Mass of flywheel (M)=10 kg. Radius (R)=50…

Q: A uniform disk of mass 2.31 kg has a radius of 0.100 m and spins with a frequency of 0.550 rev/s.…

A: Angular momentum of the uniform disk is L=Iω=12mr2ω

Q: A 646 g, 17.4 cm diameter cylinder rolls across a table at 2.00 m/s. What is the cylinder's kinetic…

A: Mass of the cylinder (M),

Q: through its centre changes from 30 rad/s to 35 rad/s, the change in angular momentum 60 kgm?/s. What…

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Q: A cylinder rotating at 11 rad/s is accelerated to 41 rad/s in 12 s. What is the angular acceleration…

A: Given data:  Initial angular velocity (ω0) = 11 rad/s Final angular velocity (ω) = 41 rad/s Time (t)…

Q: Question 2. A round object with moment of inertia Iobject = MR², mass M = 2.2 kg, and radius R=0.2 m…

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Q: A cylinder of radius 2.59 cm2.59 cm and a sphere of radius 9.22 cm9.22 cm are rolling without…

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Q: Q1. A bullet of mass m = 2.0 gram is moving horizontally with a speed v= 500.0 m/s. The bullet…

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Q: diameter

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Q: bugs, Buzz and Crunchy, are siting on a spinning disk. The disk of radius 7.5 m spins with an…

A: Angular velocity ω = 90 degrees/ sec = π/2 rad/s  = 1.57 rad/s

Q: 18. A 510-kilogram wrecking ball is free to swing from a 12 meter long wire. The ball has a maximum…

A: 18. The maximum angular displacement of the ball is very small (θ=π20 radians=1.8°). Therefore the…

Q: P rad/s 212.06 .a O

A: Given,Radius of the cylinder, R = 7.5 mangular velocity of the cylinder, ω = 9.0 rad/sec

Q: The Moon has a mass of 7.35 × 1022 kg and a radius of 1.74 × 106 m. It orbits around the Earth at a…

A: Given that :             The Moon has a mass of 7.35 × 1022 kg                    radius of moon (R)…

Q: Hi there. I need some help with this question. A car with 56-cm -diameter tires accelerates…

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Q: A turntable with a mass of 12 kg and a radius of 1.8 meters spins at a constant angular velocity of…

A:

Q: 4. A point object of mass 2m is attached to one end of a rigid rod of negligible mass and length L-4…

A: Initial momentum = mv                               = 30 m (Kg m/s)Using conservation of momentum30m…

Q: A marble rolls down the track and around a loop-the-loop of radius 0.2 m. The marble has mass 59 g…

A: Given, mass of the marble, m=59 g radius of the marble, r=1.5 cm Radius of the loop, R=0.2 m

Q: What is the instantaneous velocity of the top of the rolling cylinder? What is the angular speed of…

A: Given: Mass of a solid cylinder disk, m=1.4kg Radius, r=8.5cm Speed, v=15cm/s

Q: A car of mass 7,772 kg moves with a speed of 27 m/s on a circular track with a diameter of 797 m.…

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Q: ball on a string has a moment of inertia of 12.5 kg · m2. It experiences a torque of 5 m N.…

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Q: A disk of radius r= 89.9 cm and rotational inertia, about the disk axis on which it is fixed, is 6.4…

A: Given Data : The radius of the circular disc is given as r=89.9 cm1m100cm=0.899 m The rotational…

Q: 0 R circular hoop of radius 25.0 cm and mass 75.0 g is rotates at 250 rpm about its radial axis as…

A: The radius of the hoop Mass of the hoop Angular Speed

Q: The following figure shows the cross section of a cylinder of radius 8.8 m rotating about its axis…

A: Given, Radius of cylinder  r= 8.8m Angular velocity    w= 4 rad/s We have,  Velocity at a point V =…

Q: A turntable with a mass of 12 kg and a radius of 1.8 meters spins at a constant angular velocity of…

A: Given, Mass of turntable, m=12kg Radius, R=1.8m Angular velocity, ω=140rpm Mass of brick, M=3kg…

Q: A solid cylindrical disk whose mass is 1.4kg and radius is 8.5cm, rolls across a horizontal table at…

A: The instantaneous velocity of the top of the rolling cylinder is calculated as, Here, vcom…

Q: The disk, which has a mass of 27 kg, is subjected to the couple moment of M = (1.7θ + 4.5) N m,…

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Q: A rotating bar's angular position is changing over time as 24.1t2 radians from time, t=0.0s. What is…

A: Given A rotating bar's angular position is changing over time as 24.1t2 radians from time, t=0.0s.…

Q: A sphere, centred on the origin, has radius 31.7 cm, and is spinning at 3 revolutions per second…

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Q: Wind generated 6.6% of the world’s electricity in 2021. The large-scale turbines generally rotate at…

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Q: A thin rod (mass 245 g) capable of rotation along a vertical axis running through its centre is…

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Q: A uniform disk of mass 5.20 kg has a radius of 0.150 m and spins with a frequency of 0.650 rev/s.…

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Q: A particle moves that is defined by the parametric equations x = 3t² - 1 y = t³ — 3t² +t-3 (where x…

A: Given data: Parametric equations: x=3t2-1 y=t3-3t2+t-3   To Find:  Angular velocity at t = 2 s, ω…

Q: An 8.70-cm-diameter, 400 g solid sphere is released from rest at the top of a 1.50-m-long, 19.0 ∘…

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Q: Ex. 56: A light meter rod has two point masses each of 2 kg fixed at its ends. If the system rotates…

A: To find- Rotational K.E. Given- Point masses attached to two ends of rod=m1=m2=2 Angular speed ω=0.5…

Q: Two bugs, Buzz and Crunchy, are siting on a spinning disk. The disk of radius 3.1 m spins with an…

A: Given, radius of the disc, R = 3.1 m angular speed, ω = 90 degreesec = π2 rads

Q: A footballer kicks a ball of mass 0.4 kg and radius 11 cm such that 33 joules of kinetic energy…

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Q: A disc (thin cylinder) of mass 0.31 kg and radius 0.57 m is rotating on a frictionless axle at a…

A: Given: The mass of the first disc is 0.31 kg. The radius of the first disc is 0.57 m. The mass of…

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.