If a particle with mass m moves with position ! r(t), then, the angular momentum is...
If a particle with mass m moves with position ! r(t), then, the angular momentum is defined as ! L(t) = m! r(t) × ! v (t) and its torque is ! τ (t) = m! r(t) × ! a(t). Show that ! L′(t) = ! τ (t) . What are the consequences for both ! a(t) and ! L(t) when ! τ (t) = ! 0 for all t?
THIS IS CALC 3 VECTOR STUFF MUST USE CALCULUS
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If a particle with mass m moves with position ! r(t), then, the
angular momentum is...
12. The angular position of the particle is (t)= 2 + 3t+ t(rad), its angular velocity...
12. The angular position of the particle is (t)= 2 + 3t+ t(rad), its angular velocity at t = 3s is: * 5 (8 Points) none of them 22 1/s 16 1/s 25 1/5 9 1/3 13.A 2.50-kg particle moves in the xy plane with a velocity of v = 3 i +5k (m/s). Determine the angular momentum of the particle in Js, when its position vector is r = 7 i (m): * (7 points) 87,5j 21j none of...
Tutorial: Angular Momentum and Torque III. Angular Momentum The angular momentum of a point particle is...
Tutorial: Angular Momentum and Torque III. Angular Momentum The angular momentum of a point particle is defined by: L = ixp. Here, is a vector that points from the point of rotation (or point around which the angular momentum is calculated) to the location of the particle and p = mb is the linear momentum of the particle. A Your little brother Joey is playing with his toy airplane. The airplane is tied to a string and its motor makes...
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has...
Mechanics.
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
A particle P with mass 5 kg has position vector r(r = 7.0 m) and velocity...
A particle P with mass 5 kg has position vector r(r = 7.0 m) and velocity v(v = 5.0 m/s) as shown in the figure. It is acted on by force F(f = 8.0 N). All three vectors is in the xy plane. About the origin, what is the z-component of the angular momentum of the particle? About the origin, what is the z-component of the torque acting on the particle? About the origin, what is the z-component of the...
A particle moves and its vector is given by ? = ??? + (? − ??)?...
A particle moves and its vector is given by ? = ??? + (? − ??)? find (a) a unit vector normal to the trajectory at t =1 (b) The angular momentum ? = ? × ??̇ of the particle where ?̇ = ?r/?t (c) The torque ? = ? × ??̈ on the particle where ?̈= ???/??2 Note: from (b) and (c) it is easily seen that ? = ?l/?t Please show all workings out and thanks for your...
A 1.30-kg particle moves in the xy plane with a velocity of = (4.10 î − 3.80 ĵ) m/s. Determine the angular momentum of...
A 1.30-kg particle moves in the xy plane with a
velocity of = (4.10
î − 3.80 ĵ) m/s. Determine the
angular momentum of the particle about the origin when its position
vector is = (1.50
î + 2.20 ĵ) m.
(b) Suppose that a particle of mass m travels along a path r(t) with velocity t)...
(b) Suppose that a particle of mass m travels along a path r(t) with velocity t) according to Newton's second law, F(t)ma(t), where a-is the acceleration. Then the angular momentum C of the particle about the origin is defined as while the torque of the force F about the origin is Show that the rate of change of the angular momentum is given by C()-T What happens to the momentum if the force F is a central force field, .e.,...
The position vector of a particle whose mass is 3.0 kg is given by: r =...
The position vector of a particle whose mass is 3.0 kg is given by: r = 4 0i + 3.0t^2 j +10k, where r is in meters and t is in seconds. Determine the angular moment and the net torque about the origin acting on the particle. Two particles M_1 = 6.5 kg and M_2 = 3.1 kg are traveling with the velocities as shown below Determine the net angular momentum and use the right rule to determine its direction
A particle of mass m moves in a circle of radius R at a constant speed...
A particle of mass m moves in a circle of radius
R at a constant speed v, as shown below. The
motion begins at point Q at time t = 0. Determine
the angular momentum of the particle about the axis perpendicular
to the page through point P as a function of time. (Use
any variable or symbol stated above along with the following as
necessary: t.)
A 1.30-kg particle moves in the xy plane with a velocity of V - (3.90 i...
A 1.30-kg particle moves in the xy plane with a velocity of V - (3.90 i 3.20j) m/s. Determine the angular momentum of the particle about the origin when its position vector is r-(1.50i2.20 j) m. R)kg m2/s
12. The angular position of the particle is (t)= 2 + 3t+ t(rad), its angular velocity at t = 3s is: * 5 (8 Points) none of them 22 1/s 16 1/s 25 1/5 9 1/3 13.A 2.50-kg particle moves in the xy plane with a velocity of v = 3 i +5k (m/s). Determine the angular momentum of the particle in Js, when its position vector is r = 7 i (m): * (7 points) 87,5j 21j none of...
Tutorial: Angular Momentum and Torque III. Angular Momentum The angular momentum of a point particle is defined by: L = ixp. Here, is a vector that points from the point of rotation (or point around which the angular momentum is calculated) to the location of the particle and p = mb is the linear momentum of the particle. A Your little brother Joey is playing with his toy airplane. The airplane is tied to a string and its motor makes...
Mechanics.
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
A particle P with mass 5 kg has position vector r(r = 7.0 m) and velocity v(v = 5.0 m/s) as shown in the figure. It is acted on by force F(f = 8.0 N). All three vectors is in the xy plane. About the origin, what is the z-component of the angular momentum of the particle? About the origin, what is the z-component of the torque acting on the particle? About the origin, what is the z-component of the...
A 1.30-kg particle moves in the xy plane with a
velocity of = (4.10
î − 3.80 ĵ) m/s. Determine the
angular momentum of the particle about the origin when its position
vector is = (1.50
î + 2.20 ĵ) m.
(b) Suppose that a particle of mass m travels along a path r(t) with velocity t) according to Newton's second law, F(t)ma(t), where a-is the acceleration. Then the angular momentum C of the particle about the origin is defined as while the torque of the force F about the origin is Show that the rate of change of the angular momentum is given by C()-T What happens to the momentum if the force F is a central force field, .e.,...
The position vector of a particle whose mass is 3.0 kg is given by: r = 4 0i + 3.0t^2 j +10k, where r is in meters and t is in seconds. Determine the angular moment and the net torque about the origin acting on the particle. Two particles M_1 = 6.5 kg and M_2 = 3.1 kg are traveling with the velocities as shown below Determine the net angular momentum and use the right rule to determine its direction
A particle of mass m moves in a circle of radius
R at a constant speed v, as shown below. The
motion begins at point Q at time t = 0. Determine
the angular momentum of the particle about the axis perpendicular
to the page through point P as a function of time. (Use
any variable or symbol stated above along with the following as
necessary: t.)
A 1.30-kg particle moves in the xy plane with a velocity of V - (3.90 i 3.20j) m/s. Determine the angular momentum of the particle about the origin when its position vector is r-(1.50i2.20 j) m. R)kg m2/s
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