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4. A non-uniform rod has total mass M and length L with mass density a=Br", where...
Example 10.8 Rotating Rod A uniform rod of length L 1.6 m and mass 2.8 k...
Example 10.8 Rotating Rod A uniform rod of length L 1.6 m and mass 2.8 k is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in the figure. The rod is released from rest in the horizontal position. What are the initial angular acceleration of the rod and the initial translational acceleration of its right end Pivot SOLVE IT Mg A rod is free to rotate around...
4(12 points) A uniform rod of length L and mass M is attached at one end...
4(12 points) A uniform rod of length L and mass M is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in Figure. The rod is released from rest in the horizontal position. (a)What are the initial angular acceleration of the rod and the initial translational acceleration of its right end (as shown in Fig.a)? (b)What is its angular speed when the rod reaches its lowest position (as...
A uniform rod with a mass m and length L has one end attached to a...
A uniform rod with a mass m and length L has one end attached to a pivot. The rod swings around on a frictionless horizontal table with angular speed wo. A ball with mass m (so same mass as the rod) is placed on the table a distance d from the pivot. The ball is made of clay so when the rod strikes it, the ball sticks to the rod (i.e., inelastic collision). If the final (post-collision) angular velocity of...
1. A thin rod of length L and total mass M has a linear mass density...
1. A thin rod of length L and total mass M has a linear mass density that varies with position as λ(x)-γ?, where x = 0 is located at the left end of the rod and γ has dimensions M/L3. ĮNote: requires calculus] (a) Find γ in terms of the total mass M and the length L. (b) Calculate the moment of inertia of this rod about an axis through its left end, oriented perpen dicular to the rod; expressed...
Problem 3. (24 points) A uniform rod of mass M and length d is free to...
Problem 3. (24 points) A uniform rod of mass M and length d is free to pivot about one end. The moment of inertia of the rod about the pivot is I = Md2/3, and the rod's center of mass is at its midpoint. The rod is released from rest at angle above the horizontal, then rotates downward under the influence of gravity. d x e When the rod reaches angle below the horizontal, determine (a) (4 points) the rotational...
A rod of mass M and length L pivots at x=0, the rod is not uniform...
A rod of mass M and length L pivots at x=0, the rod is not uniform in density and follows the equation e=1+x (kg/m). What is the momentum of inertia in the rod
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al)....
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al). A point mass m is placed at distance x from one end of the rod, along the axis of the rod. Calculate the gravitational force of the rod on the point mass m. (Hint: element of the mass is dM = adx) -GmM/x? O-GmM/(L2-x2) -GmM/(x+.5L) -GmM/(x2+Lx)
For Problems 2 -3: A thin rod of total length L has non-uniform charge density given...
For Problems 2 -3: A thin rod of total length L has non-uniform charge density given by 0 wherex- 0 is at the center of the rod P2. (a) Describe in this charge distribution words (b) If the total charge on this rod is Q, determine o P3. Determine the electric field a distance d past the end of the rod. Does your answer depend on which end?
A uniform rod of mass M = 5.14kg and length L = 1.01m can pivot freely...
A uniform rod of mass M = 5.14kg and length L = 1.01m can pivot
freely (i.e., we ignore friction) about a hinge attached to a wall,
as seen in the figure below.
The rod is held horizontally
and then released. At the moment of release, determine the angular
acceleration of the rod. Use units of rad/s^2.
Determine the linear acceleration of the tip of the rod. Assume
that the force of gravity acts at the center of mass of...
A wooden board of length L and total mass m has a linear mass density λ...
A wooden board of length L and total mass m has a linear mass density λ = α x3. • A.) Find the constant α in terms of L and m. • B.) Find the center of mass of the board in terms of the given algebraic variables. Assume the left end of the board is placed at x = zero. • C.) If the pivot point is placed at the center of the board and a block of mass...
Example 10.8 Rotating Rod A uniform rod of length L 1.6 m and mass 2.8 k is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in the figure. The rod is released from rest in the horizontal position. What are the initial angular acceleration of the rod and the initial translational acceleration of its right end Pivot SOLVE IT Mg A rod is free to rotate around...
4(12 points) A uniform rod of length L and mass M is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in Figure. The rod is released from rest in the horizontal position. (a)What are the initial angular acceleration of the rod and the initial translational acceleration of its right end (as shown in Fig.a)? (b)What is its angular speed when the rod reaches its lowest position (as...
A uniform rod with a mass m and length L has one end attached to a pivot. The rod swings around on a frictionless horizontal table with angular speed wo. A ball with mass m (so same mass as the rod) is placed on the table a distance d from the pivot. The ball is made of clay so when the rod strikes it, the ball sticks to the rod (i.e., inelastic collision). If the final (post-collision) angular velocity of...
1. A thin rod of length L and total mass M has a linear mass density that varies with position as λ(x)-γ?, where x = 0 is located at the left end of the rod and γ has dimensions M/L3. ĮNote: requires calculus] (a) Find γ in terms of the total mass M and the length L. (b) Calculate the moment of inertia of this rod about an axis through its left end, oriented perpen dicular to the rod; expressed...
Problem 3. (24 points) A uniform rod of mass M and length d is free to pivot about one end. The moment of inertia of the rod about the pivot is I = Md2/3, and the rod's center of mass is at its midpoint. The rod is released from rest at angle above the horizontal, then rotates downward under the influence of gravity. d x e When the rod reaches angle below the horizontal, determine (a) (4 points) the rotational...
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al). A point mass m is placed at distance x from one end of the rod, along the axis of the rod. Calculate the gravitational force of the rod on the point mass m. (Hint: element of the mass is dM = adx) -GmM/x? O-GmM/(L2-x2) -GmM/(x+.5L) -GmM/(x2+Lx)
For Problems 2 -3: A thin rod of total length L has non-uniform charge density given by 0 wherex- 0 is at the center of the rod P2. (a) Describe in this charge distribution words (b) If the total charge on this rod is Q, determine o P3. Determine the electric field a distance d past the end of the rod. Does your answer depend on which end?
A uniform rod of mass M = 5.14kg and length L = 1.01m can pivot
freely (i.e., we ignore friction) about a hinge attached to a wall,
as seen in the figure below.
The rod is held horizontally
and then released. At the moment of release, determine the angular
acceleration of the rod. Use units of rad/s^2.
Determine the linear acceleration of the tip of the rod. Assume
that the force of gravity acts at the center of mass of...
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