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#1 A particle of mass, m, moves along the path with its coordinates given as functions...
(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.,...
2. A particle moves in the x-y plane. Its coordinates are given as functions of time...
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
A 1.6 kg particle moves in a circle of radius 3.1 m. As you look down...
A 1.6 kg particle moves in a circle of radius 3.1 m. As you look down on the plane of its orbit, the particle is initially moving clockwise. If we call the clockwise direction positive, the particle's angular momentum relative to the center of the circle varies with time according to L(t) = 10 N · m·s - (5.0 N · m)t. (a) Find the magnitude and direction of the torque acting on the particle in N · m. Is...
Please explain clearly. I need to know each steps reasons. 5) (Kepler's Problem) Suppose that a...
Please explain clearly. I need to know each steps
reasons.
5) (Kepler's Problem) Suppose that a particle is moving in three dimensions under the influence of the force k F=- where k is a positive constant. (a) Find the torque acting on the particle with respect to the origin. Is angular momentum conserved? Show that the magnitude of the angular momentum is given by l = mr2ė. (b) Using Newton's second law, show that the momentum of the particle is...
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the b...
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. B. Compute the magnitude of that force. HINT. Start with finding the angular velocity o [rad/s] of the body (the rate of...
1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8...
Acceleration in polar coordinates is required
1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8)--, expressed in plane polar coordinates. The angle 6(t) changes with time according to the equation θ wt. Here a, are positive constants independent of time. (a) [10 marks) Compute the transverse acceleration of the particle (b) [10 marks) Find the force acting on a particle and express it in terms...
There is an object, which moves in a circular path with radius of 0.367 m and...
There is an object, which moves in a circular path with radius of 0.367 m and angular acceleration of 0.12 rad/s a) If the object starts at rest find the time required to get angular velocity of 1.52 rad/s? (2 points) b) Find net linear acceleration of the object at the time of angular velocity of 1.32 rad/s? (4 points) At a particular instant, a 1.5 kg particle's position is r = (21-4j+6k)m, its velocity is Y = (-3i+5j +2k)...
4. A particle moves along the curve y = A12 so that its position is given...
4. A particle moves along the curve y = A12 so that its position is given by x = Bt. (a) Find the position vector of the particle in the form 式t) = x(t) + y(t) j (b) Calculate the speed u = of the particle along this path at an arbitrary instant t.
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...
(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.,...
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
Please explain clearly. I need to know each steps
reasons.
5) (Kepler's Problem) Suppose that a particle is moving in three dimensions under the influence of the force k F=- where k is a positive constant. (a) Find the torque acting on the particle with respect to the origin. Is angular momentum conserved? Show that the magnitude of the angular momentum is given by l = mr2ė. (b) Using Newton's second law, show that the momentum of the particle is...
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. B. Compute the magnitude of that force. HINT. Start with finding the angular velocity o [rad/s] of the body (the rate of...
Acceleration in polar coordinates is required
1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8)--, expressed in plane polar coordinates. The angle 6(t) changes with time according to the equation θ wt. Here a, are positive constants independent of time. (a) [10 marks) Compute the transverse acceleration of the particle (b) [10 marks) Find the force acting on a particle and express it in terms...
There is an object, which moves in a circular path with radius of 0.367 m and angular acceleration of 0.12 rad/s a) If the object starts at rest find the time required to get angular velocity of 1.52 rad/s? (2 points) b) Find net linear acceleration of the object at the time of angular velocity of 1.32 rad/s? (4 points) At a particular instant, a 1.5 kg particle's position is r = (21-4j+6k)m, its velocity is Y = (-3i+5j +2k)...
4. A particle moves along the curve y = A12 so that its position is given by x = Bt. (a) Find the position vector of the particle in the form 式t) = x(t) + y(t) j (b) Calculate the speed u = of the particle along this path at an arbitrary instant t.
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...
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