Concept explainers
(a)
To Calculate: The moment of inertia of combination of platform-drum.
(a)
Answer to Problem 82P
The moment of inertia of combination of platform-drum is
Explanation of Solution
Given data:
Radius of the concentric drum,
Mass of the hanging object,
Distance through which the object falls,
Time,
Formula used:
Torque,
Where, I is the moment of inertia and
From Newton’s second law of motion:
Where, F represents force, m represents mass and a represents acceleration.
Second equation of motion is:
Where, s is the displacement, t is the time, a is the acceleration and
Calculation:
Apply the Newton’s second law of motion to the platform
Apply the Newton’s second law of motion to the weight:
Relation between angular acceleration and acceleration is
Substituting for
Now, substituting for the tension in equation
The relation among the distance, acceleration and time is given by
The intial velocity
Substitute for the initial velocity
The moment of inertia of combinaiton of platform-drum is:
Conclusion:
The moment of inertia of combination of platform-drum is
(b)
To Calculate: The total moment of inertia.
(b)
Answer to Problem 82P
The total moment of inertia is
Explanation of Solution
Given data:
Radius of the concentric drum,
Mass of the hanging object,
Distance fall by the object,
Time,
Formula used:
From the previous part:
Calculation:
Substitute the values and solve for total moment of inertia:
Conclusion:
Total moment of inertia is
(c)
To Calculate: The moment of inertia of the object.
(c)
Answer to Problem 82P
The moment of inertia of the object is
Explanation of Solution
Given data:
The total moment of inertia is
The moment of inertia of combination of platform-drum is
Formula used:
The moment of inertia of the object can be calculated by using the formula:
Calculation:
Moment of inertia of the object,
Conclusion:
Moment of inertia of the object is
Want to see more full solutions like this?
Chapter 9 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
- To develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of 60.0°. (a) What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.250kg-m2 and the net force she exerts is 750 N at an effective perpendicular lever arm of 2.00 cm? (b) How much work does she do?arrow_forwardA giant swing at an amusement park consists of a 365-kg uniform arm 10.0 m long, with two seats of negligible mass connected at the lower end of the arm (Fig. P8.53). (a) How far from the upper end is the center of mass of the arm? (b) The gravitational potential energy of the arm is the same as if all its mass were concentrated at the center of mass. If the arm is raised through a 45.0 angle, find the gravitational potential energy, where the zero level is taken to be 10.0 m below the axis, (c) The arm drops from rest from the position described in part (b). Find the gravitational potential energy of the system when it reaches the vertical orientation. (d) Find the speed of the seats at the bottom of the swing.arrow_forwardThe 11 kg disk has an angular velocity of w = 20 rad/s. (Figure 1) Figure 400 mm 500 mm 200 mm- A B ⒸO 500 mm с P (N) 5 2 1 of 1 -t(s) Part A If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is μ = 0.4. Neglect the thickness of the brake. Express your answer to three significant figures and include the appropriate units. t = 0 Submit Value μA Provide Feedback Request Answer Units ? Next >arrow_forward
- Q2: (a) A particle of mass m moves under the influence of the force F = a(sinwtî + coswtſ). If the particle initially at rest at the origin. Prove that work done at any time t is given by W = mw? =(1– coswt) and that the instantaneous power applied is - sinwt. ma? (b) Find the moment of inertia of a ring of radius a about an axis through its center.arrow_forwardReleasing a frictionless box and a rolling disk with equal masses from the top of identical inclined planes, how much sooner does the box reach the bottom of the incline than the disk? Express your answer in terms of some or all of the variables m, h, θ, and R, as well as g. We know: The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy.arrow_forwardThe 11 kg disk has an angular velocity of w = 20 rad/s. (Figure 1) Figure 400 mm 500 mm. 200 mm- ↓ B 500 mm -- P (N) 2 -t(s) 1 of 1 If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is μk = 0.4. Neglect the thickness of the brake. Express your answer to three significant figures and include the appropriate units. t = 5.86 μА X Incorrect; Try Again; Provide Feedback S ? Nexarrow_forward
- A meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end just before it hits the floor, assuming that the end on the floor does not slip. (Hint: Consider the stick to be a thin rod and use the conservation of energy principle.) Number i Unitsarrow_forwardBlock 1 with mass m1=502 kg rests on a horizontal ledge with negligible friction. This block is then attached to a string that passes over a pulley, and the other end of the string is attached to the hanging block 2 of mass m2=251 kg, as shown. The pulley is a uniform disk of radius 9.40 cm and mass 1.770 kg. Calculate the speed of block 2 after it is released from rest and falls a distance of 2.15 m. What is the angular speed of the pulley at the instant when block 2 has fallen a distance of 2.15 m?arrow_forwardAs a solid disk rolls over the top of a hill on a track, its speed is 60 cm/s. If friction losses are negligible, how fast is the disk moving when it is 12 cm below the top?arrow_forward
- A playground ride consists of a disk of mass M = 38 kg and radius R = 1.5 m mounted on a low-friction axle (see figure below). A child of mass m = 24 kg runs at speed v = 2.5 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. R m Marrow_forwardJill stands initially at rest on a uniform, solid carousel (disk) which is also initially at rest. Jill has a mass of 75.0 kg and the carousel has a mass of 200 kg. Jill is 15.0 m from the center of the carousel. Jill then begins to walk counterclockwise around the carousel at a constant speed of 2.00 m/s. You can treat Jill as a point object at the edge of the turntable. Ignore any frictional or resistive forces. a) What is Jill’s angular velocity (angular speed and direction) as she walks around the carousel? Show your work b) Is the angular momentum of the system of both the carousel + Jill conserved from before she begins to walk until after she begins to walk? Explain your answer c) What is the total angular momentum of the system initially (before Jill begins to walk)? Explain your answer d) Solve for the angular velocity (angular speed and direction) of the carousel after Jill begins to walk.arrow_forwardIn the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passesover a frictionless pulley of moment of inertia 0.00400 kg · m2 and radius 5.00 cm. The coefficient offriction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find thespeed of the upper block just as it has moved 0.600 m. A) 3.19 m/s B) 1.40 m/s C) 1.22 m/s D) 1.95 m/s E) 5.44 m/sarrow_forward
- College PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegePhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning