At what height h above its center G should a billiard ball of radius r be struck horizontally by a cue if the ball is to start rolling without sliding?

Q: Find the required angular speed, ω, of an ultracentrifuge for the radial acceleration of a point…

A: Given- Acceleration a =6×105g=6×105×9.8=58.8×105 m/s2  r=1.4 cm=0.014 m

Q: The small mass starts at rest and slides down the smooth surface of a cylinder of radius R. Find the…

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Q: A particle initially moves in a horizontal circular path of radius π meters at a constant speed of 4…

A: Consider the diagram shown below representing the given system. Here, r is the radius of the…

Q: A uniform disk with a radius R swings without friction about a perpendicular asxis on the rim. If it…

A: Given,Uniform disk of radius R, if we assume disk of mass M having centre of mass lie at centre and…

Q: During a certain time interval, the angular position of a rotating disk is described by =20-t+3r If…

A: Angular position of rotating disk is given by : θ = 20 - t + 3t3Diameter = 22 cm Radius = 11 cm =…

Q: A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30o. The…

A: Given:Mass of the cylinder, m = 10 kgRadius of the cylinder, r = 0.15 mAngle of inclination = 30…

Q: A cylinder is rolling without slipping up an inclined plane and slowing down. The VCOM is the linear…

A: For pure rolling the disc should rotate about point of contact. In pure rolling motion velocity of…

Q: A child of mass m stands at rest nearthe rim of a stationary merry-go-round of radius R and moment…

A: According to the law of conservation of angular momentum Where, vg: Child’s speed with respect to…

Q: Shown is a space station with a circular rim that forms the space station's main corridor or…

A: Given the acceleration of the apple is 27 km/h2.The diameter of the space station is 210 m.

Q: A particle with mass = 20 kg is initially at the center of a disk that has mass = 80 kg , radius r=…

A: Given data The mass of the disk is md=80 kg The mass of the particle is mp=20 kg The radius of the…

Q: A boy on a merry-go-round at a distance of 1.25 m from the center. If the boy moves through an arc…

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Q: The precession angular velocity of a gyroscope is 1.0 rad/s. If the mass of the rotating disk is 0.4…

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Q: A body rotates with angular velocity w, if r is the position vector of a point P on the rotating…

A: As we know,  Angular velocity is the rate at which the particle rotate around a centre point. We can…

Q: A rigid body is made of threeidentical thin rods, each with lengthL = 0.600 m, fastened together in…

A: The length of each rod,   The mass of each rod,

Q: A solid ball (Iom =MR )rolls smoothly from rest (starting at height H= 5.3 m until it leaves the…

A: H = 5.3 m h = 2.1 m t = 0.63 s Let the mass of the ball = m Let the radius of the ball = r

Q: The position vector of a particle relative to a certain point has a magnitude of 3 m, and the force…

A: Given Magnitudes Force |N| = 4 N Position vector |r| = 3 m

Q: What angle in radians is subtended by an arc that has length 2.50 m and is part of a circle of…

A: Given data:  Arc length (s) = 2.50 m Radius (r) = 1.5 m

Q: For rolling without slip, the acceration of a circular disk on an incline plane a=r(alpha) where…

A: When rolling occurs without slipping then the linear velocity of center of mass is, vcm=rω Here, r…

Q: Find the torque of a force 7iˆ + 3jˆ – 5ˆk about the origin. The forceacts on a particle whose…

A: Given:Force on particle = (7i + 3j + 5k) NPosition vector of the particle = i + j + k

Q: Find 1. the center of mass for this circle? 2. The moment of inertia about the Z axis

A: The center of mass of a sector of radius 'r' subtending an angle 2θθ at the center is given by,  z =…

Q: A rubber ball with a radius of 3.2 cm rolls along the horizontalsurface of a table with a constant…

A: The determine the constant acceleration of the motion for the position as a function time is,

Q: Find the angle θ between the vectors a=5i−j−5kand b=2i+j−2k Answer (in radians): θ=?

A: a→ = 5i^ - j^ - 5k^b→ = 2i^ + j^ - 2k^|a| = 52 + 12 + 52 |a| = 51|b| = 22 + 12 +22|b| = 3

Q: A vehicle is slowing down at a rate res of radius 0.30 m have initial angule 5 s-1, determine: a)…

A: The acceleration of  the vehicle  a = -2.5 m/s2  The radius of the tires r = 0.30 m  The initial…

Q: A particle is moving at constant speed in a circular path of radius R=1 (m) . If the position vector…

A: Given that: R=1 ω=0.7 rad/s

Q: A certain gyroscope consists of a uniform disk with a 50 cm radius mounted at the center of an axle…

A: The distance r from the center of the mass to the ground,

Q: t of the shape! As such the

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Q: (а) the angular displacement, (b) the angular acceleration, (c) the (linear) tangential…

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Q: The 100 kg sphere A is released from rest at an angle of a from the vertical, and hits the 10 kg…

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Q: A particle is moving in a curved path with a constant angular velocity of 2 rads-1. Which of the…

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Q: a particle P moves upward along the line x=4 with a constant speed of 2 units per second. find the…

A: The angular velocity of radius vector OP is given by v/r. ,where r isthe distance from o to P and v…

Q: A solid spherical ball starts from rest at an initial height of 1.7 m, and rolls down an incline.…

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Q: A solid cylinder with a mass of (5 kg) and a radius of (0.2 m) (I =12MR2) is initially rolling along…

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Q: What is the angle (in radians) between the vectors (1.3, -2.2, 7.1) and (1.9, 5.2, -10.0)?

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Q: A pool ball is struck directly in its center so that it begins to slide across the table without…

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Q: If an airplane propeller rotates at 2000 rev/min while the airplane flies at a speed of 480 km/h…

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Q: is given an initial velocity v = 0.2 m/s. The maximum angular speed, O'max, is:

A: It is given that a simple pendulum with L=2m Initial velocity =0.2m/s

Q: At the instant shown, the 50-kg projectile travels in the vertical plane with a speed of v=40 m/s.…

A: Tangential direction force is defined as Ft=mat Here m is mass and at is tangential acceleration.…

Q: The downward motion of an elevator is controlled by a cable that unwinds from a cylinder of radius…

A: Given data:  Linear velocity (v) = 1.2 m/s Radius (r) = 0.25 m Required: Angular velocity (ω)

Q: For a particle moving under a force field, a): Is the torque about the force zero? b): Is the…

A: Part a  For particle moving under a force field  Is the torque about the force zero false…

Q: g is wrapped around a uniform cylinder of mass M and radius R. A ball of mass m is attached to the…

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Q: Let’s approximate the motion of a yo-yo with that of a solid cylinder with a string wrapped around…

A: Given data The string length is: H = 1.2 m The mass of the cylinder is: m = 0.1 kg The radius is: r…

Q: A seat on the perimeter of a Ferris wheel at the amusement park experiences an angular displacement…

A: radius of the wheel, r= 20 mangular displacement, θ=37°( to find arc length, angle must be measured…

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).