A wheel, starting from rest, rotates with a constant angular acceleration of 2.80 rad/s2. During a certain 5.00 s interval, it turns through 65.0 rad. (a) How long had the wheel been turning before the start of the 5.00 s interval? (b) What was the angular velocity of the wheel at the start of the 5.00 s interval?

2 answers
Question:

A wheel, starting from rest, rotates with a constant angular acceleration of 2.80 rad/s2. During a certain 5.00 s interval, it turns through 65.0 rad. (a) How long had the wheel been turning before the start of the 5.00 s interval? (b) What was the angular velocity of the wheel at the start of the 5.00 s interval?

Answers

Answer:a) time t1 = 2.14sb) initial angular speed w1 = 6 rad/sExplanation:Given that;Initial Angular velocity = w1 Angular distance = s = 65 radtime = t = 5 sAngular acceleration a = 2.80 rad/s^2Using the equation of motion;s = w1t + (at^2)/2w1 = (s-0.5(at^2))/tSubstituting the values;w1 = (65 - (0.5×2.8×5^2))/5w1 = 6rad/sTime to reach w1 from rest;w1 = at1t1 = w1/a = 6/2.8 = 2.14sa) time t1 = 2.14sb) initial angular speed w1 = 6 rad/s

Answer:a. The wheel was turning 2.14 s before the start of the 5.00 s interval.b. The angular velocity of the wheel at the start of the 5.00 s interval was 6.00 rad/s.Explanation:At the start of the 5.00s interval, the wheel might have an initial angular velocity [tex]\omega_0[/tex]. We can obtain it from the kinematic equation:[tex]\theta=\omega_0t+\frac{1}{2}\alpha t^{2}\\\\\implies \omega_0=\frac{\theta}{t}-\frac{1}{2}\alpha t[/tex]Plugging in the known values for the time interval, the angular displacement and the angular acceleration, we get:[tex]\omega_0=\frac{65.0rad}{5.00s}-\frac{1}{2}(2.80rad/s^{2})(5.00s)\\\\\omega_0=6.00rad/s[/tex]It means that the angular velocity of the wheel at the start of the 5.00 s interval was 6.00 rad/s (b).The time it took for the wheel to reach that angular velocity can be obtained from another kinematic equation:[tex]\omega = \omega_0+\alpha t\\\\\implies t=\frac{\omega-\omega_0}{\alpha}[/tex]It is important to take in account that in this case, the initial angular velocity is zero as the wheel started from rest, and the final angular velocity is the one we got in the previous question:[tex]t=\frac{6.00rad/s-0}{2.80rad/s^{2}}\\\\t=2.14s[/tex]Finally, the wheel was turning 2.14 s before the start of the 5.00 s interval (a).

Similar Solved Questions

2 answers

What would most likely be the result of a malfunctioning liver? • difficultly passing urine • inability to grow hair •buildup of toxins •limited feces production

What would most likely be the result of a malfunctioning liver? • difficultly passing urine • inability to grow hair •buildup of toxins •limited feces production...
1 answer

Joan Osborne is evaluating a potential capital investment. She has calculated the net present value using a minimum rate of return of 10%. Using this rate, the net present value is negative. What does this tell her about the rate of return expected for the project

Joan Osborne is evaluating a potential capital investment. She has calculated the net present value using a minimum rate of return of 10%. Using this rate, the net present value is negative. What does this tell her about the rate of return expected for the project...
1 answer

Help me out ples!!!!!!!!!!

Help me out ples!!!!!!!!!!...
1 answer

This tool (refer to the graphic), which helps the Ritz-Carlton (a luxury hotel) is known as the Zone of Tolerance concept. Its purpose is to:_________ a) evaluate employee performance in a service context b) evaluate the quality of its service relative to that of competitors c) understand consumer behavior in a service context d) measure financial performance of a service

This tool (refer to the graphic), which helps the Ritz-Carlton (a luxury hotel) is known as the Zone of Tolerance concept. Its purpose is to:_________ a) evaluate employee performance in a service context b) evaluate the quality of its service relative to that of competitors c) understand consume...
1 answer

State the Third Law of Motion on the basis of the Third law explain the following [a] A boat tend to leave the shore when passengers are alighting from it. [b] The rocket moves upwards with high speed. [c] The air filled balloon moves vertically upwards when released.

State the Third Law of Motion on the basis of the Third law explain the following [a] A boat tend to leave the shore when passengers are alighting from it. [b] The rocket moves upwards with high speed. [c] The air filled balloon moves vertically upwards when released....
2 answers

One World History MC.

One World History MC....
2 answers

Classify the terms as related to a thermal system or mechanical system. Conduction, Motion, Distance, Temperature, Absolute Zero, and Speed.

Classify the terms as related to a thermal system or mechanical system. Conduction, Motion, Distance, Temperature, Absolute Zero, and Speed....
1 answer

What year did New Mexico officially become a U.S. state?

What year did New Mexico officially become a U.S. state?...
2 answers

Work out the circumference of a circle with radius 7.5 cm take pi to be 3.142

Work out the circumference of a circle with radius 7.5 cm take pi to be 3.142...
1 answer

A mass has a final velocity of 200 m/s from rest with and acceleration of 6 m/s 2. How long did it take ?

A mass has a final velocity of 200 m/s from rest with and acceleration of 6 m/s 2. How long did it take ?...
1 answer

Name all capitals and countries North africa & middle east

Name all capitals and countries North africa & middle east...
2 answers

What is the mean absolute deviation of the data set? {0, 0, 0, 5, 0}

What is the mean absolute deviation of the data set? {0, 0, 0, 5, 0}...
2 answers

According to the author, what is the main reason for the decrease in trillium in the forest? What evidence does she give to support her claim?

According to the author, what is the main reason for the decrease in trillium in the forest? What evidence does she give to support her claim?...
1 answer

Through: (1,0), slope=1

through: (1,0), slope=1...
2 answers

18. Which tool of the biologist is more suitable for culturing bacteria in thelaboratory?A. Test tubesC. Perti dishesB. MicroscopesD. Beakers​

18. Which tool of the biologist is more suitable for culturing bacteria in thelaboratory?A. Test tubesC. Perti dishesB. MicroscopesD. Beakers​...
1 answer

Find x in the given figure​

find x in the given figure​...
1 answer

Describe the social impact of the 14th amendment

describe the social impact of the 14th amendment...
1 answer

Select the correct answer.What was William Shakespeare's initial motive for becoming an actA.He wanted to provide money for his family.B. He wanted to be famous.O c.He wanted to elevate his status in society.D.He wanted to fulfill his parents' wishes.​

Select the correct answer.What was William Shakespeare's initial motive for becoming an actA.He wanted to provide money for his family.B. He wanted to be famous.O c.He wanted to elevate his status in society.D.He wanted to fulfill his parents' wishes.​...
1 answer

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date. Truie or False

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date. Truie or False...
1 answer

What is 8 divided by 1 4/5

What is 8 divided by 1 4/5...

-- 0.044362--