Find the torque about the origin when a force of 31 N acts on the particle whose position vector is 2km.

Q: At what height h above its center G should a billiard ball of radius r be struck horizontally by a…

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Q: A bicycle tire of radius 5.1meter  rotates {theta}radian in time 6.9 seconds. Calculate the…

A: Given: The radius of the tire is r=5.1 m. The number of rotations is θ. The time taken to complete…

Q: Find the torque about the origin when a force of 3j N acts on a particle whose position vector is 2k…

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Q: The following angles are given in radians. Convert them todegrees: p>6, 0.70p, 1.5p, 5p.

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Q: A small object with mass 4.45 kg moves counterclockwise with constant speed 1.60 rad/s in a circle…

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Q: = (8.55 N )i – (9.95 N Jk acts on a pebble with position vector = (6.87 m )j – m )k, relative to the…

A: Torque τ = r̅ × F̅

Q: Find the angle between the vectors u = 5i - 9j and v = /5i+j- 3k. The angle between the vectors is…

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Q: What is the angle in radians between the vectors a=(7,-7,1) and b

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Q: A vector force with components (1, 2, 3) acts at the point (3, 2, 1). Find the vector torque about…

A: Given: The component pf force is F=(1,2,3). The component of point is r=(3,2,1). At origin ro=…

Q: A force of F = 3i + 0.5j – 5k), N is applied to a particle located at r = 2i +4k, m. Determine a)…

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Q: A wheel 2.15 m in diameter lies in a vertical plane and rotates about its central axis with a…

A: It is given that, d=2.15 mr=d2=1.075 mα=4.10 rad/s2θ=57.3o=1 radt=2 sωf=8.2 rad/sv=8.815 m/s

Q: Force F= (-7.5 N )i + (4.8 N) acts on a particle with position vector = (2.1 m )i + (3.3 m ) 7. What…

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Q: Find the angle between the vectors u = -i- 5j and v = 4i + 6j – 4k. The angle between the vectors is…

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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: Given the vectors S=3i + 2j and T= -2i + 2j; using the rotational product, find the angle

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Q: The force F = 2i − j − 5k acts at the point (−5, 2, 1). Find the torque due to Fabout the origin and…

A: The point on which force is applied can be given as, The position vector about the origin is,

Q: Force F= (-8 N)i + (6 N)j acts on a particle with position vector r= (3 m)i + (4 m)j. What are (a)…

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Q: A force F = 2i − 3j + k acts at the point (1, 5, 2). Find the torque due to F(a) about the…

A: (a) The position vector of the force about the origin is, The torque about the origin can be given…

Q: The following angles are given in degrees. Convert them to radian: 30°, 45°, 60°, 90°, 180°.

A: The relation between angle in degrees and radian is; 180°=π rad1°=π180 rad

Q: A 234 kg boat is negotiating a circular turn (radius = 33.1 m) around a buoy.  During the turn, the…

A: Given data *The mass of the boat is m = 234 kg *The radius of the circular turn is r = 33.1 m *The…

Q: What is the magnitude of the torque about the origin? b) What is the magnitude of the torque about…

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Q: A small object with mass 4.45 kg moves counterclockwise with constant speed 1.60 rad/s in a circle…

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Q: A force vector (2, -1, 4)N acts on a particle at the position (1, -3, 0)m. What is the torque due to…

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Q: Force F = (- 7.7 N )i + (4.6 N )j acts on a particle with position vector = (2.5 m )i + (4.2 m )j.…

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Q: Force É = (- 5.5 N )î + (2.9 N j acts on a particle with position vector 7 = (4.3 m )î + (8.3 m .…

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Q: Force F = (8.55 N )î – (9.95 N )ê acts on a pebble with position vector T (6.87 m )ĵ – (2.53 m )k,…

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Q: Force F = (-7.0 N)î + (5.0 N) ĵ acts on a particle with position vector 7 = (4.0 m)î + (5.0 m) ĵ.…

A: The problem can be solved as follows

Q: Consider the 12 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with…

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Q: 25 N ¡30° T 20° 45° 2.0 m C 10 N 一4.0 m- 30 N

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Q: A small object with mass 3.80 kg moves counterclockwise with constant speed 1.70 rad/s in a circle…

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Q: A small object with mass 4.00 kg moves counterclockwise with constant angular speed 1.50 rad/s in a…

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Q: (a) What is the angular speed v about the polar axis of a point on Earth’s surface at latitude 40…

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Q: What is the angle between the vectors a = (10, -10, 0) and b = (-5, 5, 2), in radians?

A: Given data: Vector a = (10, - 10, 0) Vector B = (-5, 5, 2) Required: Angle between the vectors

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).