**Pulley Experiment: Determining the Moment of Inertia**You have a pulley with a diameter of 12.6 cm and a mass of 2.0 kg. You are curious whether the mass of the pulley is uniformly distributed, or if it is concentrated towards the center or the rim. To investigate, the following experiment can be conducted:1. Hang the pulley on a hook.2. Wrap a string around it several times.3. Attach your 1.4 kg physics book to the end of the string.4. Position the book 1.5 m above the floor.5. Use a stopwatch to record the time taken for the book to hit the floor, which you find to be 0.68 s.Use the acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \).**Questions:**1. What is the moment of inertia if the pulley is uniform? - Provide your answer in the input box (units: kg m\(^2\)).2. What is the actual moment of inertia of the pulley based on your measurement? - Provide your answer in the input box (units: kg m\(^2\)).This exercise aims to deepen your understanding of rotational dynamics and the distribution of mass in rotating objects.

Answered: Image /qna-images/answer/8eeb2fa3-4381-4e1d-a67f-c02cfd6a89ce.jpg

You have a pulley 12.6 cm in diameter and with a mass of 2.0 kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is it concentrated toward the center or the rim? To find out, you hang the pulley on a hook, wrap a string around it several times, and suspend your 1.4 kg physics book 1.5 m above the floor. With your stopwatch, you can find that it takes 0.68 s for your book to hit the floor. Use g=9.8 m/s2. What is the moment of inertia if the pulley is uniform? X kg m2 What is the actual moment of inertia of the pulley based on your measurement? X kg m2

You have a pulley 12.6 cm in diameter and with a mass of 2.0 kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is it concentrated toward the center or the rim? To find out, you hang the pulley on a hook, wrap a string around it several times, and suspend your 1.4 kg physics book 1.5 m above the floor. With your stopwatch, you can find that it takes 0.68 s for your book to hit the floor. Use g=9.8 m/s2. What is the moment of inertia if the pulley is uniform? X kg m2 What is the actual moment of inertia of the pulley based on your measurement? X kg m2

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter10: Rotational Motion And Angular Momentum

Section: Chapter Questions

Problem 19PE: Unreasonable Results A gymnast doing a forward flip lands on the mat and exerts a 500- Nm torque to...

See similar textbooks

Related questions

Q: A meter stick (a uniform thin rod of length 1.0 m and mass 0.30 kg) is placed on a fulcrum at the 61…

A: Let l denotes the meterstick length, m denotes the meterstick mass, r denotes the pivot distance, x…

Q: The diameter of the base of a tapered drinking cup is 6 cm. The diameter of its mouth is 9 cm. The…

Q: A trap-jaw ant has mandibles that can snap shut with some force, as you might expect from its name.…

A: The force is approx. 167.12 times the weight of ant.

Q: A meter stick has a mass of 0.18 kg and balances at its center. When a small chain is suspended from…

A: Given:- The mass of the meter stick is M = 0.18 kg The meter stick is balanced at its center. A…

Q: A uniform solid ball rolls smoothly along a floor, then up a ramp inclined at 15.0°. It momentarily…

Q: A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The…

A: L = 0.877 m m = 1.23 kg Initial angular velocity = 0 rad/secFinal angular velocity = 6.61 rad/sec…

Q: meter stick has a fixed axis of rotation at 50 m. A 4 kg mass is located at the 10 m marker, a 5 kg…

A: Length of the meter stick is L = 50 m For the system to be in equilibrium, the net torque of the…

Q: A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm (I =…

Q: A 400 N, 8 meter long rod is attached to a wall and supported by a cable as shown below. A 27 kg…

Q: A 10-m long homogenous beam with a weight of 50N is divided into 10 equal parts (1 m each) as shown…

Q: A participant in a "strongman" competition uses an old-fashioned device to move a large load with…

Q: A 0.5 kg meter stick has a center of mass at the 50 cm mark. You place a pivot at the 50 cm mark and…

Q: a makeshift close-grip pull-up station. The I beam is anchored at two points (Point A) is at one…

A: We are given the mass of man. We hence know the weight of man. We first apply equilibrium of torque…

Q: A piece of metal is pressed against the rim of a 3.2- kg, 18- cm-diameter grinding wheel that is…

A: Given: The mass of the wheel is 3.2 kg. The diameter of the wheel is 18 cm. The coefficient of…

Q: The 20-mm-diameter A-36 steel shaft is subjected to the torques shown. 80 Nm 20 Nm 30 Nm 800 mm 600…

Q: John is pushing his daughter Rachel in a wheelbarrow when it is stopped by a brick 8.00 cm high (see…

Q: A metal hoop with 0.21 kg of mass and 0.060 m of radius rolled without slipping on a horizontal…

Q: A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The…

Q: In the figure below, both the ceiling and the ruler accelerate together at 2.7 m/s2 in the +y…

A: Given Data: Acceleration of the system , a=2.7ms2 in +y direction. Weight of the pan , Wp=6N.…

Q: A spindle is wrapped with a very fine silk thread and is sitting initially at rest on a horizontal…

A: (A)Consider the spindle as a solid cylinder, so the moment of inertia of the spindle is,Substitute…

Q: John is pushing his daughter Rachel in a wheelbarrow when it is stopped by a brick 8.00 cm high (see…

Q: cat is balanced on the edge of a see-saw. The plank of the see-saw is 1m long, and the wedge is…

Q: A solid uniform 45-kg ball of diameter 32.0 cm is supported against a vertical, frictionless wall…

Q: A ruler with the length of 100 cm and mass of 100g has the pivot point at 35 Cm. Jason suspends an…

Q: cylinder box 10m

Q: A 4.0- m-long iron bar of uniform cross section is held perpendicular to the wall by a wire from the…

Q: A uniform meterstick is in static rotational equilibrium when a mass of 220 g is suspended from the…

A: Given,

Q: The wheels,axle, and handles of a wheelbarrow weigh W=56N. The load chamber and it’s contents weigh…

A: Given Data: Weight (W) = 56 N.Weight of the load chamber WL = 635 N. To Determine: The magnitude of…

Q: A meter stick balances horizontally on a knife-edge at the 50.0 cm mark. With two 6.35 g coins…

Q: A coke can is suspended by a string from the tab so that it spins with a vertical axis. A 14 N…

Q: A string holds and wraps around a solid cylinder (7-kg and R = 3-m). A person pulls the string…

Q: A 9 m long board that has a mass of 14. Each end is held up by a vertical rope. A 45 kg box sits 1 m…

A: Given length of long board L = 9m Mass of board M = 14 kg Mass of box m = 45 kg Distance of the box…

Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Pulley Experiment: Determining the Moment of Inertia**

You have a pulley with a diameter of 12.6 cm and a mass of 2.0 kg. You are curious whether the mass of the pulley is uniformly distributed, or if it is concentrated towards the center or the rim. To investigate, the following experiment can be conducted:

1. Hang the pulley on a hook.
2. Wrap a string around it several times.
3. Attach your 1.4 kg physics book to the end of the string.
4. Position the book 1.5 m above the floor.
5. Use a stopwatch to record the time taken for the book to hit the floor, which you find to be 0.68 s.

Use the acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \).

**Questions:**

1. What is the moment of inertia if the pulley is uniform?
- Provide your answer in the input box (units: kg m\(^2\)).

2. What is the actual moment of inertia of the pulley based on your measurement?
- Provide your answer in the input box (units: kg m\(^2\)).

This exercise aims to deepen your understanding of rotational dynamics and the distribution of mass in rotating objects.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is ML2/3 Why is this moment of inertia greater than it would be if you spun a point mass M at the location of the center of mass of the rod (at L/2)? (That would be ML2/4.)
As shown in Figure OQ10.7, a cord is wrapped onto a cylindrical reel mounted on a fixed, friction less, horizontal axle. When does the reel have a greater magnitude of angular acceleration? (a) When the cord is pulled down with a constant force of 50 N. (b) When an object of weight 50 X is hung from the cord and released, (c) The angular accelerations in parts (a) and (b) are equal, (d) It is impossible to determine.
Review. As shown in Figure P10.77, two blocks are connected by a string of negligible mass passing over a pulley of radius r= 0.250 m and moment of inertia I. The block on the frictionless incline is moving with a constant acceleration of magnitude a = 2.00 m/s2. From this information, we wish to find the moment of inertia of the pulley. (a) What analysis model is appropriate for the blocks? (b) What analysis model is appropriate for the pulley? (c) From the analysis model in part (a), find the tension T1(d) Similarly, find the tension T2. (e) From the analysis model in part (b), find a symbolic expression for the moment of inertia of the pulley in terms of the tensions T1 and T2. the pulley radius r, and the acceleration a. (f) Find the numerical value of the moment of inertia of the pulley.
Additional Problems A typical propeller of a turbine used to generate electricity from the wind consists of three blades as in Figure P8.75. Each blade has a length of L = 35 in and a mass of m = 420 kg. The propeller rotates at the rate of 25 rev/min. (a) Convert the angular speed of the propeller to units of rad/s. Find (b) the moment of inertia of the propeller about the axis of rotation and (c) the total kinetic, energy of the propeller. Figure P8.75
A boy stands at the center of a platform that is rotating without friction at 1.0 rev/s. The boy holds weights as far from his body as possible. At this position the total moment of inertia of the boy, platform, and weights is 5.0kgm2 . The boy draws the weights in close to his body, thereby decreasing the total moment of inertia to 1.5kgm2 . (a) What Is the final angular velocity of the platform? (b) By how much does the rotational kinetic energy increase?
Four objects are held in position at the corners of a rectangle by light rods as shown in Figure P8.37. Find the moment of inertia of the system about (a) the x-axis, (b) they-axis, and (c) an axis through O and perpendicular to the page.
While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75kg-m2 and its rotational kinetic energy is 175 J. (a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter's shoe if it is 1.05 m from the hip joint? (c) Explain how the football can be given a velocity greater than the tip of the shoe (necessary for a decent kick distance).
(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges? There is only one pair of hinges.
A spool of thread consists of a cylinder of radius R1 with end caps of radius R2 as depicted in the end view shown in Figure P10.45. The mass of the spool, including the thread, is m, and its moment of inertia about an axis through its center is I. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T acting to the right is applied to the free end of the thread. (a) Show that the magnitude of the friction force exerted by the surface on the spool is given by f=(I+mR1R2I+mR22)T (b) Determine the direction of the force of friction. Figure P10.45
Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximately a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.
A disk of mass m , radius R , and area A has a surface mass density =mrAR (see the following figure). What is the moment of inertia of the disk about an axis through the center?
A simple pendulum consists of a small object of mass 3.0 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 5.0 angle with the vertical. (b) Does the torque increase or decrease as the angle increases? Explain. Figure P8.6