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A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion?
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A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for ...
**Solution:**
Given:
- Initial angular velocity, $\omega_1 = 20 \text{ rpm}$
- Final angular velocity, $\omega_2 = ?$
- Time interval, $t = 70 \text{ seconds}$
- Number of revolutions, $N = 1$
**a) Angular Velocity at the End of Interval**
We know that the angular velocity is given by the formula:
$$\omega = \frac{2\pi N}{t}$$
Substituting the given values, we have:
$$20 \text{ rpm} = \frac{2\pi \times 1}{70} \text{ rad/s}$$
Therefore, the angular velocity at the end of the interval is $20 \text{ rpm}$.
**b) Time required to reach 100 rpm**
We can find the time required to reach a certain angular velocity using the formula:
$$\omega = \frac{2\pi N}{t}$$
Rearranging the formula, we get:
$$t = \frac{2\pi N}{\omega}$$
Substituting the given values, we have:
$$t = \frac{2\pi \times 1}{100} \text{ seconds}$$
Therefore, the time required to reach a speed of $100 \text{ rpm}$ is $\frac{2\pi}{100}$ seconds.
**c) Angular Retardation to Completely Stop after One Minute**
To calculate the angular retardation required to completely stop after one minute, we need to find the final angular velocity after one minute.
Using the formula:
$$\omega = \frac{2\pi N}{t}$$
Substituting the given values, we have:
$$100 \text{ rpm} = \frac{2\pi \times 1}{60} \text{ rad/s}$$
Now, the angular retardation can be calculated using the formula:
$$\text{Retardation} = \frac{\omega - \omega_0}{t}$$
Substituting the given values, we have:
$$\text{Retardation} = \frac{\frac{2\pi}{60} - \frac{2\pi}{70}}{60} \text{ rad/s}^2$$
**d) Total Angular Displacement**
The total angular displacement can be calculated using the formula:
$$\theta = \frac{1}{2}(\omega + \omega_0)t$$
Substituting the given values, we have:
$$\theta = \frac{1}{2} \left(\frac{2\pi}{60} + \frac{2\pi}{70}\right) \times 60 \text{ radians}$$
Simplifying the expression, we get:
$$\theta = \frac{\pi}{42} \text{ radians}$$
Therefore, the total angular displacement is $\frac{\pi}{42}$ radians.
Given:
- Initial angular velocity, $\omega_1 = 20 \text{ rpm}$
- Final angular velocity, $\omega_2 = ?$
- Time interval, $t = 70 \text{ seconds}$
- Number of revolutions, $N = 1$
**a) Angular Velocity at the End of Interval**
We know that the angular velocity is given by the formula:
$$\omega = \frac{2\pi N}{t}$$
Substituting the given values, we have:
$$20 \text{ rpm} = \frac{2\pi \times 1}{70} \text{ rad/s}$$
Therefore, the angular velocity at the end of the interval is $20 \text{ rpm}$.
**b) Time required to reach 100 rpm**
We can find the time required to reach a certain angular velocity using the formula:
$$\omega = \frac{2\pi N}{t}$$
Rearranging the formula, we get:
$$t = \frac{2\pi N}{\omega}$$
Substituting the given values, we have:
$$t = \frac{2\pi \times 1}{100} \text{ seconds}$$
Therefore, the time required to reach a speed of $100 \text{ rpm}$ is $\frac{2\pi}{100}$ seconds.
**c) Angular Retardation to Completely Stop after One Minute**
To calculate the angular retardation required to completely stop after one minute, we need to find the final angular velocity after one minute.
Using the formula:
$$\omega = \frac{2\pi N}{t}$$
Substituting the given values, we have:
$$100 \text{ rpm} = \frac{2\pi \times 1}{60} \text{ rad/s}$$
Now, the angular retardation can be calculated using the formula:
$$\text{Retardation} = \frac{\omega - \omega_0}{t}$$
Substituting the given values, we have:
$$\text{Retardation} = \frac{\frac{2\pi}{60} - \frac{2\pi}{70}}{60} \text{ rad/s}^2$$
**d) Total Angular Displacement**
The total angular displacement can be calculated using the formula:
$$\theta = \frac{1}{2}(\omega + \omega_0)t$$
Substituting the given values, we have:
$$\theta = \frac{1}{2} \left(\frac{2\pi}{60} + \frac{2\pi}{70}\right) \times 60 \text{ radians}$$
Simplifying the expression, we get:
$$\theta = \frac{\pi}{42} \text{ radians}$$
Therefore, the total angular displacement is $\frac{\pi}{42}$ radians.
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A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion?
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A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion?.
A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel rotating abt a fixed axis at 20rpm is uniform accelerated for 70 seconds , during which time it makes revolution. Find a) angular velocity at the end of interval b ) Time required (from rest) for the speed to reach 100rpm. c) After the wheel reach the speed of 100rpm , it is expected to decelerate And completely stop exactly after one minute. calculate The uniform angular retardation required for this purpose d) Find the total angular displacement of the motion?.
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