3, 4, 5 ### Rotational Dynamics Problem SetA solid disk with a mass of 7.0 kg and a radius of 30 cm gradually increases its rotational speed from 45 revolutions per minute (rpm) to 120 rpm over a period of 5.0 seconds. Analyze the following questions based on this scenario:3. **Find the angular acceleration in rad/s².**4. **Calculate the number of revolutions the disk completes in these 5.0 seconds.**5. **Determine the change in rotational kinetic energy.**6. **Calculate the moment of inertia of the disk in kg·m².**7. **Find the magnitude of torque needed to achieve the change in rpm.**8. **Calculate the tangential acceleration of a point \( P \) on the outer rim of the disk.**#### Diagram ExplanationThe accompanying diagram illustrates a solid disk. The disk has a radius \( R \) and rotates about its center. It shows the angular velocity \( \omega \) and angular acceleration \( \alpha \). Point \( P \) is marked on the outer rim, indicating the location where tangential acceleration needs to be calculated.

Name: 3, 4, 5 ### Rotational Dynamics Problem SetA solid disk with a mass of
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: 3, 4, 5 ### Rotational Dynamics Problem SetA solid disk with a mass of 7.0 kg and a radius of 30 cm gradually increases its rotational speed from 45 revolutions per minute (rpm) to 120 rpm over a period of 5.0 seconds. Analyze the following questions

Given: m = 7 kg r = 30 cm = 0.30 m w0 = 45 rpm =45* 2pi/60 rad/s w = 120 rpm = 120*2pi/60 rad/s t = 5 s (3) alpha= (w-w0)/t = ((120- 45)*2pi/60)/5 = 1.57 rad/s^2 (4) th = w0t + 1/2*alpha*t^2 = (45*2pi/60)*5 + (1/2*1.57*5^2) = 43.2 rad = 43.2/2pi rev = 6.87 rev (5) I = 1/2*mr^2 =1/2*7*0.30^2 = 0.315 kg-m^2 dKE = 1/2*I*(w^2 - w0^2) = 1/2*0.315*((120*2pi/60)^2 - (45*2pi/60)^2) = 21.4 J

Science

Physics

A solid disk of mass equal to 7.0 kg and radius of 30 cm changes its rotations gradually from 45 rpm to 120 rpm in 5.0 sec. 3. find the angular acceleration in rad/s². 4. how many revolutions has the disk turned in this 5.0 seconds? 5. find the change in rotational kinetic energy.

A solid disk of mass equal to 7.0 kg and radius of 30 cm changes its rotations gradually from 45 rpm to 120 rpm in 5.0 sec. 3. find the angular acceleration in rad/s². 4. how many revolutions has the disk turned in this 5.0 seconds? 5. find the change in rotational kinetic energy.

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: 2. Determine the sum and the difference of the two unit vectors below: R= B+ C R = B+ C and R= B- C*…

Q: 6. Calculate and draw (on the graph above) the sum of the two vectors from above (r₁ + r₂) and the…

A: Here r1→=3i^-2j^r2→=i^+3j^Now,r1→+r2→=(3+1)i^+(-2+3)j^=4i^+j^r1→-r2→=(3-1)i^+(-2-3)j^=2i^-5j^

Q: Find a unit vector with a magnitude of 1 that points in the same direction as the vector…

A: The objective of the question is to find a unit vector that points in the same direction as the…

Q: Q2 (a) Based on the straight current-carrying filamentary conductor of length AB as can be viewed in…

A: (a) Given: OA=OB=1m, I=8A Refer to the figure below :

Q: x (cm) 3.0 2.0 1.0 -1.0 -2.0 -3.0 0.50 1.0 A 2.41 kg ball is attached to an unknown spring and…

Q: Don't use chatgpt will upvote

A: Part (a) Determine the unit vector that defines the direction of FABDetermine the coordinates of…

Q: if A=-2i+3j-4k C=-2j+4i find (A+C).(AXC)

A: A = -2 i + 3 j - 4 k C = - 2 j + 4 i

Q: Given two vectors A = 9.97 i + 1.92 j- 1.56 k, B = 0.05 i - 7.08 j+ 4.89 k, find the %3D magnitude…

Q: 4) Two vectors, A= 2x 3y and B= 4x 4y. The magnitude of A+B is: A) 4.3 B) 5.1 C) 7.8 D) 6.4 E) 9.2

A: A→=2x^-3y^B→=4x^-4y^where x^ and y^ are unit vectors along x and y directionso…

Q: Vector A has x, y, and z components given by 7, 2, and 5 units. What is the angle the vector makes…

A: Given Ax = 7 units Ay = 2 units Az = 5 units

Q: Assuming the +x-axis is horizontal to the right for the vectors in the following figure, find the…

A: a)Resolve vector A into respective x and y components as,

Q: Explain the difference between a scalar and a vector with a detailed explanation.

A: Scalar quantities are those which only have magnitude and no direction. It can be considered as…

Q: 2. A hiker walking 10 km west then 25 km south

A: Required answer of problem(2)

Q: What is the angle between the vector A = +3i - 2i - 3k and the +y-axis?

A: Given:Vector are,A→=3i^-2j^-3 k^ ...(1)B→=Along y-axisB→=y^=j^ .... (2)We know,cosθ=A→.B→|A||B|…

Q: A vector quantity is described with a direction and a scalar is not Select one: O True O False

A: Answer -: true Vector quantity describes by direction and magnitude both.

Q: two vectors perpendicular

Q: Problem 4 A sailboat sails 25 km to the north and then 65 km in the direction 34° west of south.…

Q: Find the Vector projection of A= and B=

A: Given, Vectors, A = 2, 1, 5, B= 5, -2, 7 The vector projection of vector A→ on vector B→ is…

Q: 15. A certain vector in the xy plane has an x component of 4 m and a y component of 10 m. It is then…

Q: You are adding two vectors, one has a magnitude of 25 and the other has a magnitude of 10. Which of…

A: Given: Magnitude of a→=25. Magnitude of b→=25. To find: The resultant vector.

Q: Complete the following conversion of the vector in P(x, y, z) to. a ) Ρ(ρ, φ, 2) b) P(r,0,4) in the…

A: (a) The conversion of the vector P from the cartesian coordinates to spherical coordinates in…

Q: Two vectors are given as follows: A -3i + 6j – 5k; B = -2i . What is the magnitude of the sum of the…

Q: How many of the vectors have a horizontal component other than 0?

A: In the given diagram, d2 vector is acting along y-axis. Hence, its horizontal component is 0. For…

Q: 27. Review. A 5.75-kg object passes through the origin at time t = 0 such that its x component of…

Q: The vector in the figure has a length of 4.0 units and makes a 30° angle with respect to the y-axis.…

Q: Find the result of the expression

A: Given, 2,1Lx2,0we…

Q: A finite segment of a straight wire carrying current I in z-direction is shown in the figure. (a)…

Q: A vector is given as follows: -37-27-3 The vector product x7 equals: O A +37 + 37 OB. 37 +27 - 37…

A: The cross product of similar unit vectors i^, j^ and k^ can be given as, i^×i^ = j^ ×j^ = k^×k^ = 0…

Q: 2 Dante plays basketball. After 3 games, he had scored 25 points and after 7 games he had scored 60…

A: Solution: Let's first calculate the number of points Dante scores per game on average. To do this,…

Q: Use the information about vectors S and T provided below in the following exercises. T.x=0m |T|= 10m…

A: Disclaimer: “Since you have asked posted a question with multiple sub-parts, we will solve the first…

Q: 2)Given the vectors A =3 î +2 ĵ and B = î -3ĵ…

A: According to guidelines we need to solve only first question kindly repost other questions in the…

Q: The scalar product A B of the two vectors A = 2i + 3j and B = i– 2j is * O -4 k O 2i - 6j 8 k

Q: Why is the angle less enic geome IS metry)

A: Geometry is the branch of units & dimensions that deals with shapes, angles, dimensions, and…

Q: Question 5 A vector has an x-component of 4 m and makes an angle of 22° counterclockwise from the…

Q: The x component of vector is -8.0 units, and its y component is 3.2 units. The magnitude of is…

Q: 4. Vector d = (-2.5, -3.6) m, reconcile the vector to polar coordinate

A: Given value--- vector d = ( -2.5 , -3.6 ) . We have to find--- polar coordinate?

Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

Topic Video

Question

3, 4, 5

### Rotational Dynamics Problem Set

A solid disk with a mass of 7.0 kg and a radius of 30 cm gradually increases its rotational speed from 45 revolutions per minute (rpm) to 120 rpm over a period of 5.0 seconds. Analyze the following questions based on this scenario:

3. **Find the angular acceleration in rad/s².**

4. **Calculate the number of revolutions the disk completes in these 5.0 seconds.**

5. **Determine the change in rotational kinetic energy.**

6. **Calculate the moment of inertia of the disk in kg·m².**

7. **Find the magnitude of torque needed to achieve the change in rpm.**

8. **Calculate the tangential acceleration of a point \( P \) on the outer rim of the disk.**

#### Diagram Explanation

The accompanying diagram illustrates a solid disk. The disk has a radius \( R \) and rotates about its center. It shows the angular velocity \( \omega \) and angular acceleration \( \alpha \). Point \( P \) is marked on the outer rim, indicating the location where tangential acceleration needs to be calculated.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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

Given the two vectors A = ( 5.5i - 3j) and B = (-9i - 8j) determine the following: A. Vector C = A + B in vector notation, it's magnitude and its direction counterclockwise from the +x-axis. B. Vector D = A - B in Vector notation, it's magnitude and its direction counterclockwise from the +x-axis.
What is the angle between two vectors A = 4i + 12j + 6k and B = 24i %3D - 8j +6k? -84.64 degrees 86.32 degrees 168.45 degrees 84.32 degrees
Question: Given vectors, which one is correct? A) C+5- A+E B) C-B= A- B D. B. D) C-5-A+ B E) Č+B = Ã - E
Adj Express the force F in Cartesian vector from if Point B is located 2m along the rode 6 m (2-1) 6 m O F = 600 N 6 m 4m 3m
주= 4.00↑ + 구.001 %3D 3 = 5.00i - 2.00j Find -> a) vector product Ax B cexpressed in unit vectors) 6.) magnitude of the vector product %3D
What is the length of a vector having these coordinates: (3, 5,-2) ?
Question: The polar coordinates of a point are 50m and . Then, what are its Cartesian coordinates? A. 2.75i+ 4.763j m, B. -2.75i- 4.763j m, C. 2.75i - 4.763j m, D. 4.763j m, E. -2.75i + 4.763j m,
7. DETAILS Two points in the xy plane have Cartesian coordinates (4.00, -3.50) m and (-7.50, 7.50) m. (a) Determine the distance between these points. m (b) Determine their polar coordinates. (4.00, -3.50) r = (4.00, -3.50) 0 = (-7.50, 7.50) r = (-7.50, 7.50) 0 = A m o counterclockwise from the +x-axis. m counterclockwise from the +x-axis MY NOTES ASK YOUR TEACHER
(D − 2)2y = 16
X AND Y COMPONENT