Tangential acceleration of a point on a rotating disk:a = RaHere is an example of rotational motion:Try another version >Example 1A block with mass m = 5.5 kg is connected to a pulley byrope (see figure). The pulley has a radius of R = 0.3 m, amoment of inertia equal to I = 9.6 kg m², and it can rotatewithout friction on its axis.Initially, the block is at a height of h 15 m above theground. At time t = 0 the system starts to move and theblock starts to move down.In this problem use g = 9.8 m/s².m1a) Determine the acceleration of the block.answer=Check your answerShow solutionnot yet solvedunits? C Show solution1b) Determine the tension in the rope while the block is falling.units? Canswer =Check your answerShow solution1c) With what speed does the block hit the ground?units? Canswer=Check your answerShow solutionanswer=1d) At what time t does the block hit the ground?units? CCheck your answerShow solutionnot yet solvedanswer=not yet solvedCheck your answerShow solution1e) What is the angular speed of the pulley at the moment theblock hits the ground?not yet solvednot yet solvedunits? CInstead of using forces and torque, we can sometimes use theconcept of energy instead.

Mass of block, m=5.5 kg Radius of pulley, R=0.3 m Moment of inertia of pulley, Ipulley=9.6 kg m2…

Try another version > Example 1 A block with mass m = 5.5 kg is connected to a pulley by rope (see figure). The pulley has a radius of R = 0.3 m, a moment of inertia equal to I = 9.6 kg m², and it can rotate without friction on its axis.

Try another version > Example 1 A block with mass m = 5.5 kg is connected to a pulley by rope (see figure). The pulley has a radius of R = 0.3 m, a moment of inertia equal to I = 9.6 kg m², and it can rotate without friction on its axis.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Two blocks having different masses m1 and m2 are connected by a string passing over a pulley as…

A: Let the 2 blocks initially are at height 0 m. Then the heights of m1 and m2 after system released…

Q: 3. A hoop and a solid sphere are released from the top of a ramp at the same time. The objects have…

Q: t end. The greit rce on the d s center of as Pot OLUTION Conceptualize Imagine what happens to the…

Q: Insert Draw Design Layout V Tell me 2 Share Verdana v10 vA A A evA. Paragraph Styles te Dictat Ge n…

Q: A hollow ball having a mass of m=5.00kg and a moment of inertia of (2/3)mr² rolls a distance d =…

A: Apply principle of conservation of energy…

Q: A new truck has tires with a diameter of 31.1 inches. The tires have a tread-life warranty of 55,000…

A: Diameter of truck tire is 31.1 inches.Life of tyre = 55000miles.

Q: Question 4 A disc is rotating horizontally about its central axis. The disc has a radius of 2.0 m, a…

Q: After 12.0 s, a spinning roulette wheel has slowed down to an angular velocity of 2.58 rad/s. During…

Q: ▼ Part A What is the moment of inertia of the wheel for an axis perpendicular to the wheel at its…

A: To find the moment of inertia of the wheel, we can use the conservation of energy principle. The…

Q: The disk starts at wo = 4 rad/s when 0 - 0, and is given an angular acceleration c = (0.30) rad/s²,…

Q: A uniform cylindrical turntable of radius 1.80 m and mass 26.1 kg rotates counterclockwise in a…

Q: In the figure, a 7.84 g bullet is fired into a 0.418 kg block attached to the end of a 0.972 m…

A: Given:Mbullet=7.84×10-3 kgMblock=0.418 kgLrod=0.972 mMrod=0.453 kgIrod=0.0636 kg.m2Find A) what then…

Q: In the figure, two 6.50 kg blocks are connected by a massless string over a pulley of radius 2.40 cm…

Q: The uniform solid block in the figure has mass 24.3 kg and edge lengths a = 0.952 m, b = 1.68 m, and…

Q: Constat You are rebuilding a 1965 Chevrolet. To decide whether to replace the flywheel with a newer,…

A: (a) a=dvdta=ddtddt(165t2)a=ddt(165)(2t)a=165(2)a=330 cm/s2=3.30 m/s2As acceleration is independent…

Q: Determine the moment of inertia of a 7.50 kg sphere of radius 0.451 m when the axis of rotation is…

A: Given data: A sphere Mass (m) = 7.50 kg Radius (r) = 0.451 m Required: Moment of inertia about…

Q: (e) Consider the conditions in parts (a) and (b) of the problem. Shortly after the collision between…

A: Angular momentum is given as L = Iω Where ω is angular velocity The direction of angular momentum…

Q: A 1.1kg bike wheel, is spinning 190rpm clockwise when a student applies a Frictional force as shown.…

A: Mass ( m ) = 1.1 kg Speed ( N ) = 190 rpm Force ( F ) = 2.3 N Radius ( r ) =( 5 × 10 ) cm = 0.5 m […

Q: Part A A string is wrapped several times around the rim of a small hoop with radius 8.00 cm and mass…

A: Answer: The angular speed of the rotating is 26.25rad/s. The speed of its center is 2.1m/s. Given…

Q: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to…

A: Disk B: Initial angular velocity: ωBi = 550 rpm = 550 × 2 π 60= 57.59 rad/s (cw) Radius…

Q: A car is traveling along the circular curve of radius r = 400ft. At the instant shown, its angular…

A: Given data:- Radius of the circular curve is r=400 ft =121.91 m Angular rate of rotation is…

Q: The uniform solid block in the figure has mass 23.7 kg and edge lengths a=0.826 m, b = 1.37 m, and…

Q: A horizontal 4.00-m long, 7.00-kg uniform beam that lies along the east-west direction is acted on…

Q: The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed…

A: Firstly, to solve the question, we have to find the acceleration while speeding up and slowing down.

Q: Problem 1 Two blocks, one of mass m₁ = 3.0 kg.and the other of mass m₂ = 9.0 kg, are slung over a…

Q: A dentist causes the bit of a high-speed drill to accelerate from an angular rad/s. In the process,…

A: Initial angular speed, ω = 1.61×10⁴ rad/sFinal angular speed, ω' = 5.21×10⁴ rad/sAngular…

Q: Ball, mass m, radius r, moment of inertia I. H path of center of · - ball A ball, of mass m, radius…

A: According to the law of conservation of energy , energy can neither be created nor destroyed but can…

Q: The disk is originally rotating at wo = 19 rad/s. It is subjected to a constant angular acceleration…

Q: The wheel is moving to the right such that it has an angular velocity w = 2.4 rad/s and angular…

A: Solution: As per the given data,

Q: When a ceiling fan rotating with an angular speed of 3.56 rad/s is turned off, a frictional torque…

Q: Problem 4 A carousel at a park has a total mass of M = 3 × 103 kg and a radius R=4 m. It can be…

Q: A solid cylinder of mass M= 3.00 kg and radius R = 0.25 m starts from rest at a height of 2.00 m and…

Q: Suppose a 72-kg person stands at the edge of a 6.2-m diameter merry-go-round turntable that is…

A: Given that, mass of the person is m=72kg the diameter of the turntable is D=6.2m the moment of…

Q: Suppose the solid wheel of the figure has a mass of 300 g and rotates at 84 rad/s; it has radius 6.3…

Q: While riding a multispeed bicydle, the rider can select the radius of the rear sprocket that is foed…

Q: The uniform solid block in the figure has mass 17.8 kg and edge lengths a = 0.815 m, b = 1.63 m, and…

Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

Tangential acceleration of a point on a rotating disk:
a = Ra
Here is an example of rotational motion:
Try another version >
Example 1
A block with mass m = 5.5 kg is connected to a pulley by
rope (see figure). The pulley has a radius of R = 0.3 m, a
moment of inertia equal to I = 9.6 kg m², and it can rotate
without friction on its axis.
Initially, the block is at a height of h 15 m above the
ground. At time t = 0 the system starts to move and the
block starts to move down.
In this problem use g = 9.8 m/s².
m
1a) Determine the acceleration of the block.
answer=
Check your answer
Show solution
not yet solved
units? C

Show solution
1b) Determine the tension in the rope while the block is falling.
units? C
answer =
Check your answer
Show solution
1c) With what speed does the block hit the ground?
units? C
answer=
Check your answer
Show solution
answer=
1d) At what time t does the block hit the ground?
units? C
Check your answer
Show solution
not yet solved
answer=
not yet solved
Check your answer
Show solution
1e) What is the angular speed of the pulley at the moment the
block hits the ground?
not yet solved
not yet solved
units? C
Instead of using forces and torque, we can sometimes use the
concept of energy instead.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Free Body Diagram

VIEW

Step 3: Calculation of acceleration

VIEW

Step 4: Calculation of tension.

VIEW

Step 5: Calculation of final speed.

VIEW

Step 6: Calculation of time.

VIEW

Step 7: Calculation of

VIEW

Solution

VIEW

Step by step

Solved in 8 steps with 1 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

I Review | Constants A machine part has the shape of a solid uniform sphere of mass 255 g and diameter 4.50 cm . It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of An unwinding cable ii. Express your answer in radians per second squared. Πν ΑΣφ ? a = 9.87 rad/s? Submit Previous Answers Request Answer X Incorrect; Try Again; 7 attempts remaining Part B How long will it take to decrease its rotational speed by 26.0 rad/s ? Express your answer in seconds. ΥΠ ΑΣφ t = 2.41 Submit Previous Answers Request Answer X Incorrect; Try Again; 7 attempts remaining Provide Feedback Next >
Two objects are attached to a nearly massless rigid rod. What is the rotational inertia (moment of inertia) of the system shown? A. 4 MR^2 B. 2 MR^2 C. 6 MR^2 D. 8 MR^2
1. Find the expression for the moment of inertia of a uniform, solid disk of mass M and radius R, rotated about an axis that goes through its center as shown in the diagram below. Hint: the moment of inertia of a thin ring is given by MR2. Divide the disk into a series of rings of radius r, mass dm, and thickness dr, then integrate over the rings. Your expression should only depend on the variables M and R. 99+
A history teacher is printing out papers with instructions for a class project. Let's assume the roller inside the printer turns with an angle 0 with the given which is e(t) = At^2 – Bt^3 Allow A be 2.50 + 0.07 rad/s^2 Allow B be s 0.450 ± 0.010 rad/s^3 Find the answers to the following questions.. 1) Find the angular speed of the roller at t = 1.00 s. 2) Find the uncertainty in the angular speed of the roller, if the uncertainty in time is given as 0.05s.
Problem 1 A light rope is fixed to and wound around a pulley of mass Mp = 2.0 kg and radius r = 0.15m. A mass of m = 0.35 kg is hung from the free end of the rope. (A) If the system starts from rest and is able to rotate with negligible friction, how fast will the mass be moving after the pulley has rotated 3/4π radians? Model the pulley as a solid cylinder with the its axle through the center. Hint: Use a conservation of energy approach. Double hint: Using the Hand in Homework procedure is especially helpful for this problem. (B) Is there another set of physics concepts you could use to solve this problem and would this other approach require more or fewer steps?
Cons A constant torgue of 25 m - N is applied to the rim of a 15-kg uniform disk of radius 0.30 m. Part A What is the angular speed of the disk about an axis through its center after it rotates 2.0 revolutions from rest? Express your answer using two significant figures. Ην ΑΣφ rad/s Previous Answers Request Answer Submit X Incorrect; Try Again; 5 attempts remaining
I Review I Constants You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 35.0 cm. Starting from rest at t = 0, the flywheel rotates with constant angular acceleration 3.00 rad/s? about an axis perpendicular to the flywheel at its center. Part A If the flywheel has a density (mass per unit volume) of 8600 kg/m³, what thickness must it have to store 800 J of kinetic energy at t = 8.00 s? Express your answer with the appropriate units. HA h = Value Units Submit Request Answer
RMQ2: please answer all parts and explain steps
A thing solid cylinder has a mass 6.98kg and a length 1.66 m. What is its moment of inertia (in unit of kg.m2) when it is rotating as shown above? (please search your physics text book or other sources for the correct formula for this situation, you lab manual does not necessarily have the formula.)
The uniform solid block in the figure has mass 39.0 kg and edge lengths a = 0.763 m, b = 1.58 m, and c= 0.0730 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Rotation axis Number i Units
A wheel rolls to the right along a horizontal surface, down a ramp, then continues along a lower horizontalsurface. 1)Draw graphs for the wheel’s angular position, angular velocity, and angular acceleration as functions oftime. 2)If the wheel continues to roll without slipping through an angular displacement ϴ, how could one determine thelinear displacement of the wheel, x?
A gyroscope slows from an initial rate of 38.3 rad/s at a rate of 0.801 rad/s2. (a) How long does it take (in s) to come to rest? (b) How many revolutions does it make before stopping? rev Additional Materials O Reading