A particle of mass m is dropped from rest at t = 0 at the point (−d, 0, 0) and falls vertically in Earth's gravitational field −gĵ. (a) What is the expression for the angular momentum of the particle about the origin? (Express your answer in vector form. Use any variable or symbol stated above as necessary.) l = (b) Calculate the torque on the particle about the origin. (Express your answer in vector form. Use any variable or symbol stated above as necessary.) τ = (c) Is the torque equal to the time rate of change of the angular momentum? Yes No
A particle of mass m is dropped from rest at t = 0 at the point (−d, 0, 0) and falls vertically in Earth's gravitational field −gĵ. (a) What is the expression for the angular momentum of the particle about the origin? (Express your answer in vector form. Use any variable or symbol stated above as necessary.) l = (b) Calculate the torque on the particle about the origin. (Express your answer in vector form. Use any variable or symbol stated above as necessary.) τ = (c) Is the torque equal to the time rate of change of the angular momentum? Yes No
A particle of mass m is dropped from rest at t = 0 at the point (−d, 0, 0) and falls vertically in Earth's gravitational field −gĵ. (a) What is the expression for the angular momentum of the particle about the origin? (Express your answer in vector form. Use any variable or symbol stated above as necessary.) l = (b) Calculate the torque on the particle about the origin. (Express your answer in vector form. Use any variable or symbol stated above as necessary.) τ = (c) Is the torque equal to the time rate of change of the angular momentum? Yes No
A particle of mass m is dropped from rest at t = 0 at the point (−d, 0, 0) and falls vertically in Earth's gravitational field −gĵ.
(a) What is the expression for the angular momentum of the particle about the origin? (Express your answer in vector form. Use any variable or symbol stated above as necessary.)
l =
(b) Calculate the torque on the particle about the origin. (Express your answer in vector form. Use any variable or symbol stated above as necessary.)
τ =
(c) Is the torque equal to the time rate of change of the angular momentum?
Yes
No
Transcribed Image Text:This image illustrates a three-dimensional Cartesian coordinate system with axes labeled as \(x\), \(y\), and \(z\). The origin (where all axes intersect) is not explicitly marked but can be inferred.
- The \(x\)-axis is horizontal, extending from left to right.
- The \(y\)-axis is vertical.
- The \(z\)-axis extends perpendicularly out of the plane towards the viewer.
A point is marked on the \(x\)-axis at coordinates \((-d, 0, 0)\). Here, \(-d\) indicates a location along the negative \(x\)-axis.
From this point, a red arrow is directed downward, labeled as \(-mg\hat{\jmath}\). This suggests a force vector acting in the negative \(y\)-direction, typically representing gravitational force where \(m\) is mass, \(g\) is acceleration due to gravity, and \(\hat{\jmath}\) is the unit vector in the direction of the \(y\)-axis.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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