A rod has a length of
and a mass of 4.00 kg. A string is attached to the CM of the rod and the system is hung from the ceiling (
[link] ). The rod is displaced 10 degrees from the equilibrium position and released from rest. The rod oscillates with a period of 0.5 s. What is the torsion constant
?
(a) A rod suspended by a string from the ceiling. (b) Finding the rod’s moment of inertia.
Strategy
We are asked to find the torsion constant of the string. We first need to find the moment of inertia.
Solution
Find the moment of inertia for the CM:
Calculate the torsion constant using the equation for the period:
Significance
Like the force constant of the system of a block and a spring, the larger the torsion constant, the shorter the period.
A mass
m suspended by a wire of length
L and negligible mass is a simple pendulum and undergoes SHM for amplitudes less than about
. The period of a simple pendulum is
, where
L is the length of the string and
g is the acceleration due to gravity.
The period of a physical pendulum
can be found if the moment of inertia is known. The length between the point of rotation and the center of mass is
L .
The period of a torsional pendulum
can be found if the moment of inertia and torsion constant are known.
Conceptual questions
Pendulum clocks are made to run at the correct rate by adjusting the pendulum’s length. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain your answer.
A pendulum clock works by measuring the period of a pendulum. In the springtime the clock runs with perfect time, but in the summer and winter the length of the pendulum changes. When most materials are heated, they expand. Does the clock run too fast or too slow in the summer? What about the winter?
The period of the pendulum is
In summer, the length increases, and the period increases. If the period should be one second, but period is longer than one second in the summer, it will oscillate fewer than 60 times a minute and clock will run slow. In the winter it will run fast.
With the use of a phase shift, the position of an object may be modeled as a cosine or sine function. If given the option, which function would you choose? Assuming that the phase shift is zero, what are the initial conditions of function; that is, the initial position, velocity, and acceleration, when using a sine function? How about when a cosine function is used?
Some people think a pendulum with a period of 1.00 s can be driven with “mental energy” or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?
(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is
is moved to a location where the acceleration due to gravity is
. What is its new period? (b) Explain why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.
A pendulum with a period of 2.00000 s in one location (
) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?
(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
