Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
A light string is wound round a cylinder and carries a mass tied to it at the free end. When the mass is released, calculate (a) the linear acceleration of the descending mass and (b) the angular acceleration of the cylinder and (c) the tension in the string. Show that the acceleration of mass is less than g.
A mass is tied to a thin, light string that is wound around a cylinder. The mass is released. There is a gravitational force pulling it downward, and the tension in the string is pulling it upward. This difference between the gravitational force and the tension can be calculated to find the net forcRead more
A mass is tied to a thin, light string that is wound around a cylinder. The mass is released. There is a gravitational force pulling it downward, and the tension in the string is pulling it upward. This difference between the gravitational force and the tension can be calculated to find the net force on the mass. By Newton’s second law, this net force must equal the product of the mass and its linear acceleration.
There’s also tension in the string creating a torque in the cylinder which can be represented in terms of tension and radius of the cylinder. The angular acceleration is found to be associated with the linear acceleration of mass by the radius of the cylinder.
We can obtain the linear acceleration of the falling mass and the tension in the string by considering these relationships. The acceleration can be written as a fraction of the acceleration due to gravity, showing that it is smaller than the acceleration due to gravity. This happens because part of the gravitational force is being utilized to generate rotational motion in the cylinder, meaning that there will be a smaller linear acceleration of the mass than if it were falling freely. This whole system demonstrates principles of rotational dynamics and linear motion.
Click this link for more information: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessObtain the expression for the linear acceleration of a cylinder rolling down inclined place and hence find the condition for the cylinder to roll down without slipping.
In finding the linear acceleration of a rolling cylinder on an inclined plane, we have the forces involved-the weight of the cylinder and the frictional force. The weight can be divided into two: one along the incline and the other perpendicular to it. The friction force opposes the motion to avoidRead more
In finding the linear acceleration of a rolling cylinder on an inclined plane, we have the forces involved-the weight of the cylinder and the frictional force. The weight can be divided into two: one along the incline and the other perpendicular to it. The friction force opposes the motion to avoid sliding.
Using Newton’s second law, we analyze the net force acting along the incline on the cylinder. The net force is the difference between the component of gravitational force pulling it down the slope and the frictional force acting up the slope. This net force is also related to the linear acceleration of the cylinder.
Next, we analyze the cylinder’s rotational motion where the frictional force causes a torque around the center of mass. Torque affects the cylinder’s angular acceleration. Linear acceleration and angular acceleration for rolling without slipping are in fact related.
Integrating these considerations shows that the linear acceleration of the rolling cylinder down the incline is a fraction of gravitational acceleration. The no slipping requirement for the rolling cylinder further depends on the coefficient of static friction and the angle of the incline so that the frictional force is always quite sufficient to prevent slipping.
see more :- https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessDiscuss the importance of maintaining a clean and calm environment for Yoga practice.
Maintaining a clean, calm environment is essential for effective Yoga practice. A clutter-free space minimizes distractions, promoting focus and mindfulness. A calm setting fosters mental clarity and positivity, enhancing energy flow during Āsanas, Prānāyāma, and meditation. Such an environment encoRead more
Maintaining a clean, calm environment is essential for effective Yoga practice. A clutter-free space minimizes distractions, promoting focus and mindfulness. A calm setting fosters mental clarity and positivity, enhancing energy flow during Āsanas, Prānāyāma, and meditation. Such an environment encourages relaxation and emotional balance, creating a conducive atmosphere for holistic well-being. By prioritizing cleanliness and tranquility, practitioners can fully immerse themselves in their practice, reaping Yoga’s physical, mental, and spiritual benefits.
See lessWhat role does Kriḍa Yoga play in promoting teamwork and mindfulness?
Krīḍā Yoga blends playful activities with mindfulness, promoting teamwork, collaboration, and emotional connection. Through group-based games, participants develop mutual respect, patience, and effective communication. These interactive exercises reduce stress and enhance focus, fostering mindfulnesRead more
Krīḍā Yoga blends playful activities with mindfulness, promoting teamwork, collaboration, and emotional connection. Through group-based games, participants develop mutual respect, patience, and effective communication. These interactive exercises reduce stress and enhance focus, fostering mindfulness in an engaging manner. By encouraging a shared sense of purpose, Krīḍā Yoga builds stronger social bonds and supports emotional balance. Its innovative approach integrates Yoga’s principles with fun, creating a holistic experience for physical, mental, and social well-being.
See lessHow does mindful eating encourage better food habits?
Mindful eating encourages better food habits by focusing on the act of eating, appreciating flavors, and being attentive to hunger and fullness cues. This practice helps prevent overeating and promotes healthier portion control. By reducing distractions during meals, it fosters gratitude, enhances dRead more
Mindful eating encourages better food habits by focusing on the act of eating, appreciating flavors, and being attentive to hunger and fullness cues. This practice helps prevent overeating and promotes healthier portion control. By reducing distractions during meals, it fosters gratitude, enhances digestion, and strengthens the connection between body and mind. Mindful eating creates awareness of food’s impact, inspiring more thoughtful choices and nurturing a balanced, healthier relationship with eating.
See less