A wheel rotates clockwise about its central axis with an angular momentum of 730 kg·m2/s. At time t = 0, a torque of magnitude 23 N·m is applied to the wheel to reverse the rotation. At what time t is the angular speed zero?
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When angular speed is zero, so is the angular momentum, so the change in angular momentum (= the angular impulse) 730 kg m2/s.
From the equation Angular Impulse = Torque X time, (think of Impulse = Force X Time)
730 = 23t --> t = 730/23 = 31.7s
From the equation Angular Impulse = Torque X time, (think of Impulse = Force X Time)
730 = 23t --> t = 730/23 = 31.7s
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Let me show you the normal way to show exponents here.
730 kg·m^2/s where the ^ is shift+6.
If this were a linear problem, you would find the momentum change and then set it equal to the impulse: F*t.
In the angular situation angular impulse = torque*time.
To convince you, think of Newton'2 2nd Law: F=ma.
Therefore 1 Newton = 1 kg·m/s^2
So you can rewrite that torque 23 kg·m^2/s^2
Use that version of torque in the formula
impulse = torque*time
and solve for time.
730 kg·m^2/s where the ^ is shift+6.
If this were a linear problem, you would find the momentum change and then set it equal to the impulse: F*t.
In the angular situation angular impulse = torque*time.
To convince you, think of Newton'2 2nd Law: F=ma.
Therefore 1 Newton = 1 kg·m/s^2
So you can rewrite that torque 23 kg·m^2/s^2
Use that version of torque in the formula
impulse = torque*time
and solve for time.