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An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process?
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An electric motor is connected to a pedestal grinding wheel and is rot...
**a) Calculating the time taken to stop:**
To find the time it takes for the grinding wheel to completely stop, we can use the equation of motion for angular deceleration:
ω = ω0 + αt
Where:
ω = final angular velocity (0 rad/min, as the wheel stops)
ω0 = initial angular velocity (1.06 * 100 rev/min)
α = angular deceleration (-1.96 rad/s^2)
t = time
Rearranging the equation, we get:
t = (ω - ω0) / α
Converting the initial and final angular velocities into radian/minute:
ω0 = (1.06 * 100 rev/min) * (2π rad/rev) * (1 min/60 s) = 11.11 rad/s
ω = 0 rad/s
Substituting the values into the equation:
t = (0 - 11.11 rad/s) / (-1.96 rad/s^2) = 5.66 s
Therefore, it takes approximately 5.66 seconds for the grinding wheel to completely stop.
**b) Calculating the radians and revolutions turned:**
To find the number of radians and revolutions the wheel has turned during the time interval, we can use the equation of motion for angular displacement:
θ = ω0t + 0.5αt^2
Where:
θ = angular displacement
ω0 = initial angular velocity (11.11 rad/s)
α = angular deceleration (-1.96 rad/s^2)
t = time (5.66 s)
Substituting the values into the equation:
θ = (11.11 rad/s)(5.66 s) + 0.5(-1.96 rad/s^2)(5.66 s)^2 = -15.78 rad
The negative sign indicates that the wheel has rotated in the opposite direction.
To find the number of revolutions, we can divide the angular displacement by 2π:
Revolutions = θ / (2π) = -15.78 rad / (2π) ≈ -2.51 rev
Therefore, the wheel has turned approximately -15.78 radians and -2.51 revolutions.
**c) Calculating the time to reach regular angular speed:**
To find the time it takes for the grinding wheel to reach its regular angular speed after being switched back on, we can use the equation of motion for angular acceleration:
ω = ω0 + αt
Where:
ω = final angular velocity (1.06 * 100 rev/min)
ω0 = initial angular velocity (0 rad/s, as the wheel is initially stopped)
α = angular acceleration (2.4 rad/s^2)
t = time
Rearranging the equation, we get:
t = (ω - ω0) / α
Converting the final angular velocity into radian/minute:
ω = (1.06 * 100 rev/min) * (2π rad/rev) * (1 min/60 s) = 11.11 rad/s
Substituting the values into the equation:
t = (11.11 rad/s - 0 rad/s) / 2.4 rad/s^2 = 4.63 s
Therefore, it would take approximately 4.63 seconds for the grinding wheel to
To find the time it takes for the grinding wheel to completely stop, we can use the equation of motion for angular deceleration:
ω = ω0 + αt
Where:
ω = final angular velocity (0 rad/min, as the wheel stops)
ω0 = initial angular velocity (1.06 * 100 rev/min)
α = angular deceleration (-1.96 rad/s^2)
t = time
Rearranging the equation, we get:
t = (ω - ω0) / α
Converting the initial and final angular velocities into radian/minute:
ω0 = (1.06 * 100 rev/min) * (2π rad/rev) * (1 min/60 s) = 11.11 rad/s
ω = 0 rad/s
Substituting the values into the equation:
t = (0 - 11.11 rad/s) / (-1.96 rad/s^2) = 5.66 s
Therefore, it takes approximately 5.66 seconds for the grinding wheel to completely stop.
**b) Calculating the radians and revolutions turned:**
To find the number of radians and revolutions the wheel has turned during the time interval, we can use the equation of motion for angular displacement:
θ = ω0t + 0.5αt^2
Where:
θ = angular displacement
ω0 = initial angular velocity (11.11 rad/s)
α = angular deceleration (-1.96 rad/s^2)
t = time (5.66 s)
Substituting the values into the equation:
θ = (11.11 rad/s)(5.66 s) + 0.5(-1.96 rad/s^2)(5.66 s)^2 = -15.78 rad
The negative sign indicates that the wheel has rotated in the opposite direction.
To find the number of revolutions, we can divide the angular displacement by 2π:
Revolutions = θ / (2π) = -15.78 rad / (2π) ≈ -2.51 rev
Therefore, the wheel has turned approximately -15.78 radians and -2.51 revolutions.
**c) Calculating the time to reach regular angular speed:**
To find the time it takes for the grinding wheel to reach its regular angular speed after being switched back on, we can use the equation of motion for angular acceleration:
ω = ω0 + αt
Where:
ω = final angular velocity (1.06 * 100 rev/min)
ω0 = initial angular velocity (0 rad/s, as the wheel is initially stopped)
α = angular acceleration (2.4 rad/s^2)
t = time
Rearranging the equation, we get:
t = (ω - ω0) / α
Converting the final angular velocity into radian/minute:
ω = (1.06 * 100 rev/min) * (2π rad/rev) * (1 min/60 s) = 11.11 rad/s
Substituting the values into the equation:
t = (11.11 rad/s - 0 rad/s) / 2.4 rad/s^2 = 4.63 s
Therefore, it would take approximately 4.63 seconds for the grinding wheel to
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An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process?
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An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process?.
An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process?.
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An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process?, a detailed solution for An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process? has been provided alongside types of An electric motor is connected to a pedestal grinding wheel and is rotating at its regular angular speed of 1.06 * 100 rev/min. after some time it was switched off. the rotating wheel was decelerated uniformly at a rate of 1.96 rad/second square. a) how long does it take the grinding wheel to completely stop? b) during the time interval found above, how many radians and revolutions has the wheel turned? c) After complete stop of the wheel, the motor was switched back on. If the angular acceleration of the motor is 2.4 rad/sec square, how long it would take the wheel to get to its regular angular speed assuming no losses during this process? theory, EduRev gives you an
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