A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to a disk. The length of the rod is L and the radius of the disk is R. The mass of each object is M0.
At this point, we know: M0, L, R, and g
Part A: What is the angular acceleration of the swinging pendulum when it at angle θ relative to vertical? Counterclockwise is the positive direction. Answer in known quantities and simplify your answer.
Part B: Explain how your answer for this problem is consistent with the following:
"the second derivative of angular position is equal to a negative constant times angular position."
Homework Answers
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A pendulum swings back and forth. The pendulum is a
one-dimensional rod that is connected to...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to a disk. The length of the rod is L and the radius of the disk is R. The mass of each object is M0. At this point, we know: M0, L, R, and g Part A: What is the angular acceleration of the swinging pendulum when it at angle θ relative to vertical? Counterclockwise is the positive direction. Answer in known quantities and simplify...
A grandfather clock contains a pendulum that swings back and forth due to gravity. Model the...
A grandfather clock contains a pendulum that swings back and
forth due to gravity. Model the pendulum as a one-dimensional rod
that is connected to a solid disk. The length of the rod is
L, and the radius of the solid disk is R. The
mass of each object is .
Known: ,
L, R, g
What is the angular acceleration of the
swinging pendulum when it is at an angle
relative to the vertical, as shown? Let counterclockwise be the
positive...
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One simple pendulum and the physical pendulums (disk and rod) are suspended on the crossbar, as...
One simple pendulum and the physical pendulums (disk and rod) are suspended on the crossbar, as shown in figure. (a) Calculate the natural linear frequency of the simple pendulum, if the length of the simple pendulum is =1.6 m (b) Calculate the natural angular frequency of the disk. The radius L 5 of the disk is R=0.5 m; moment of inertia about an axis through the 0.3 R center of mass is ICM =mR2 (c) Calculate the natural period of...
2. As shown below a uniform disk of radius R 10.0 cm and mass M 0.850...
2. As shown below a uniform disk of radius R 10.0 cm and mass M 0.850 kg is attached to the end of a uniform rigid rod of length L = 500 mm and mass m = 0.210 kg. Take positive θ in the counterclockwise direction, and positive angular velocity ω as into the page. Assume small angle deflection (a) When the disk is suspended from a pivot as sown what is the period of its motion? (b) If this...
The pendulum shown below consists of a slender rod of length L and a think disk...
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In a ballistic pendulum an object of mass m is fired with an initial speed v0 at a pendulum bob.
In a ballistic pendulum an object of mass m is fired with an initial speed v0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement θ as shown.Part AFind an expression for vo, the initial speed of the fired object. Express your answer in terms of some or all of the...
A pendulum consists of a disk of mass, m, and radius, r, connected to a pivot...
A pendulum consists of a disk of mass, m, and radius, r, connected to a pivot point via string (of negligible mass) of length, l. Note, the disk hangs vertically and the string is attached to its top. For small angles, derive an expression for: (a) angular position as a function of time (b) angular velocity as a function of time (c) angular acceleration as a function of time
IVUIedl Peruuiunil. Ldiye riCLIUIT Case The equation of a pendulum having an attached mass m >...
IVUIedl Peruuiunil. Ldiye riCLIUIT Case The equation of a pendulum having an attached mass m > 0, a massless rod of length 1 > 0, and swinging in a medium with damping constant d > O is mld" = -mg sin(0) – dle', where e(t) is the angular position of the pendulum as function of time, measured from the vertical downwards position, positive counter- clockwise, and g is the acceleration of gravity. We consider the following particular case: . =...
A grandfather clock contains a pendulum that swings back and
forth due to gravity. Model the pendulum as a one-dimensional rod
that is connected to a solid disk. The length of the rod is
L, and the radius of the solid disk is R. The
mass of each object is .
Known: ,
L, R, g
What is the angular acceleration of the
swinging pendulum when it is at an angle
relative to the vertical, as shown? Let counterclockwise be the
positive...
The pendulum consists of a 7-kg slender rod with length (L) of 1.2 m and it is fixed to a 16-kg disk with radius of 0.3 m. If the spring has an un-stretched length of 0.2 m and stiffness of 200 N/m, determine the angular velocity of the pendulum when it is released from rest and rotates clockwise 90° from the position shown. The roller at C allows the spring to always remain vertical. At θ-00, the stretched length of...
One simple pendulum and the physical pendulums (disk and rod) are suspended on the crossbar, as shown in figure. (a) Calculate the natural linear frequency of the simple pendulum, if the length of the simple pendulum is =1.6 m (b) Calculate the natural angular frequency of the disk. The radius L 5 of the disk is R=0.5 m; moment of inertia about an axis through the 0.3 R center of mass is ICM =mR2 (c) Calculate the natural period of...
2. As shown below a uniform disk of radius R 10.0 cm and mass M 0.850 kg is attached to the end of a uniform rigid rod of length L = 500 mm and mass m = 0.210 kg. Take positive θ in the counterclockwise direction, and positive angular velocity ω as into the page. Assume small angle deflection (a) When the disk is suspended from a pivot as sown what is the period of its motion? (b) If this...
The pendulum shown below consists of a slender rod of length L and a think disk of radius r. If the rope connected to the disk breaks as shown, find the initial angular accleration of pendulum and the reaction forces at O. Assume Wrod = 12 lbs, Wdisk = 20 lbs, r = 2 ft, and L = 3 ft. x = Ox= rad/s 2 (1 decimal) lbs (no decimals) lbs (1 decimal) Oy = 1-1 L
IVUIedl Peruuiunil. Ldiye riCLIUIT Case The equation of a pendulum having an attached mass m > 0, a massless rod of length 1 > 0, and swinging in a medium with damping constant d > O is mld" = -mg sin(0) – dle', where e(t) is the angular position of the pendulum as function of time, measured from the vertical downwards position, positive counter- clockwise, and g is the acceleration of gravity. We consider the following particular case: . =...
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