
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 1.2 kg⋅m2 .
Explanation of Solution
Given data:
Radius of the concentric drum, R=10 cm
=(10 cm)(1 m100 cm)=0.100 m
Mass of the hanging object, M=2.50 kg
Distance through which the object falls, D=1.80 m
Time, t1=4.2 s
Formula used:
Torque, τ=Iα
Where, I is the moment of inertia and α is the angular acceleration.
From Newton’s second law of motion:
∑Fi=miai
Where, F represents force, m represents mass and a represents acceleration.
Second equation of motion is:
s=v0t+12at2
Where, s is the displacement, t is the time, a is the acceleration and v0 is the initial velocity.
Calculation:
Apply the Newton’s second law of motion to the platform
∑τ=TR =I0α .......(1)
Apply the Newton’s second law of motion to the weight:
∑Fy=Mg−T =Ma .......(2)
Relation between angular acceleration and acceleration is α=aR
Substituting for α in equation (1) then the tension in the string is
T=I0aR2
Now, substituting for the tension in equation (2) , and solve for the moment of inertia,
Mg−I0aR2=Ma I0=MR2(g−a)a=MR2(ga−1) ..........(3)
The relation among the distance, acceleration and time is given by
s=v0t+12at2
The intial velocity (v0) of the object is zero.
Substitute for the initial velocity (v0) of the object and distance in the above equation:
D=12at2a=2Dt2
The moment of inertia of combinaiton of platform-drum is: I0=MR2(gt22D−1) =(2.50 kg)(0.100 m)2((9.80m/s2)(4.20 s)22(1.80 m)−1) =1.18 kg⋅m2 ≈1.2 kg⋅m2
Conclusion:
The moment of inertia of combination of platform-drum is 1.2 kg/m2 .
(b)
To Calculate: The total moment of inertia.
(b)

Answer to Problem 82P
The total moment of inertia is 3.1 kg⋅m2 .
Explanation of Solution
Given data:
Radius of the concentric drum, R=10 cm
=(10 cm)(1 m100 cm)=0.100 m
Mass of the hanging object, M=2.50 kg
Distance fall by the object, D=1.80 m
Time, t2=6.8 s
Formula used:
From the previous part:
Itotal=MR2(gt22D−1)
Calculation:
Substitute the values and solve for total moment of inertia:
Itotal=MR2(gt22D−1) =(2.50 kg)(0.100 m)2((9.80m/s2)(6.80 s)22(1.80 m)−1) =3.1 kg⋅m2
Conclusion:
Total moment of inertia is 3.1 kg⋅m2 .
(c)
To Calculate: The moment of inertia of the object.
(c)

Answer to Problem 82P
The moment of inertia of the object is 1.9 kg⋅m2 .
Explanation of Solution
Given data:
The total moment of inertia is 3.1 kg⋅m2 .
The moment of inertia of combination of platform-drum is 1.2 kg⋅m2 .
Formula used:
The moment of inertia of the object can be calculated by using the formula:
I=Itotal−I0
Calculation:
Moment of inertia of the object, I=Itotal−I0
=3.12 kg⋅m2−1.18 kg⋅m2=1.9 kg⋅m2
Conclusion:
Moment of inertia of the object is 1.9 kg⋅m2 .
Want to see more full solutions like this?
Chapter 9 Solutions
Physics for Scientists and Engineers
- Four capacitors are connected as shown in the figure below. (Let C = 12.0 µF.) A circuit consists of four capacitors. It begins at point a before the wire splits in two directions. On the upper split, there is a capacitor C followed by a 3.00 µF capacitor. On the lower split, there is a 6.00 µF capacitor. The two splits reconnect and are followed by a 20.0 µF capacitor, which is then followed by point b. (a) Find the equivalent capacitance between points a and b. µF(b) Calculate the charge on each capacitor, taking ΔVab = 16.0 V. 20.0 µF capacitor µC 6.00 µF capacitor µC 3.00 µF capacitor µC capacitor C µCarrow_forwardTwo conductors having net charges of +14.0 µC and -14.0 µC have a potential difference of 14.0 V between them. (a) Determine the capacitance of the system. F (b) What is the potential difference between the two conductors if the charges on each are increased to +196.0 µC and -196.0 µC? Varrow_forwardPlease see the attached image and answer the set of questions with proof.arrow_forward
- How, Please type the whole transcript correctly using comma and periods as needed. I have uploaded the picture of a video on YouTube. Thanks,arrow_forwardA spectra is a graph that has amplitude on the Y-axis and frequency on the X-axis. A harmonic spectra simply draws a vertical line at each frequency that a harmonic would be produced. The height of the line indicates the amplitude at which that harmonic would be produced. If the Fo of a sound is 125 Hz, please sketch a spectra (amplitude on the Y axis, frequency on the X axis) of the harmonic series up to the 4th harmonic. Include actual values on Y and X axis.arrow_forwardSketch a sign wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forward
- Sketch a sine wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forwardThe drawing shows two long, straight wires that are suspended from the ceiling. The mass per unit length of each wire is 0.050 kg/m. Each of the four strings suspending the wires has a length of 1.2 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 20°. (a) Draw the free-body diagram showing the forces that act on the right wire with respect to the x axis. Account for each of the strings separately. (b) What is the current in each wire? 1.2 m 20° I -20° 1.2 marrow_forwardplease solve thisarrow_forward
- please solve everything in detailarrow_forward6). What is the magnitude of the potential difference across the 20-02 resistor? 10 Ω 11 V - -Imm 20 Ω 10 Ω 5.00 10 Ω a. 3.2 V b. 7.8 V C. 11 V d. 5.0 V e. 8.6 Varrow_forward2). How much energy is stored in the 50-μF capacitor when Va - V₁ = 22V? 25 µF b 25 µF 50 µFarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegeCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning





