6.2 Torque and Work

• Torque is calculated using the force, the distance from the axis, and the sine of the angle between them.


  True
• Torque is the force that causes rotational motion around a pivot point.

  True
• The formula for work includes the cosine of the angle between force and displacement.


  True
• The cosine of the angle between force and displacement determines the work done.


  True
• The formula for work includes the cosine of the angle between force and displacement.


  True
• What is the moment of inertia in the relationship between torque and angular acceleration?

  Resistance to rotation
• The relationship between torque and angular acceleration is expressed by the formula $\tau =$$I \alpha$.


  True
• If a wheel with a moment of inertia of 2 kg·m² is subjected to a torque of 5 Nm, its angular acceleration is 2.5 rad/s².
• What is the formula for work done on a rotating object?

  $W =$$\tau \theta$
• If the initial angular velocity of the flywheel in the example is 2 rad/s, its final angular velocity is 6 rad/s.

  True
• The magnitude of torque is calculated using the formula $\tau =$$rF\sin\theta$, where $\theta$ is the angle between the force and the distance.
• The relationship between torque and angular acceleration is given by the formula $\tau =$$I \alpha$, where $I$ represents the moment of inertia.
• A wheel with a moment of inertia of 3 kg·m² experiences a torque of 12 Nm over an angular displacement of 4 radians. If it starts at 2 rad/s, what is its final angular velocity?

  6 rad/s
• Rotational kinetic energy is given by the formula $KE_{rot} =$$\frac{1}{2} I \omega^{2}$, where $I$ is the moment of inertia
• $\omega_{f}$ and $\omega_{i}$ in the work-energy theorem represent the final and initial angular velocities, respectively.


  True
• What is the final angular velocity of a wheel with $I =$$3$ kg·m², starting at 2 rad/s, when a torque of 12 Nm is applied over an angular displacement of 4 radians?


  6 rad/s
• Provide an example of positive torque and negative torque in real-life situations.

  Tightening and loosening a bolt
• The work-energy theorem in rotational motion relates work to the change in rotational kinetic energy.


  True
• A disc-shaped flywheel (mass = 8 kg, radius = 0.5 m) experiences a force of 10 N applied perpendicularly at its edge, causing it to rotate through 30 radians. Calculate the work done on the flywheel.

  150 J
• The distance from the axis of rotation to the line of action of the force is called the perpendicular distance
• The perpendicular distance from the axis of rotation to the line of action of the force is called the lever arm.
• In the formula for work, 'd' represents displacement
• The perpendicular distance from the axis of rotation to the line of action of the force is called the lever arm.
• If you lift a box 5 meters vertically with a force of 20 N, how much work is done?

  100 joules
• Torque is directly proportional to angular acceleration.


  True
• In the formula $\tau =$$I \alpha$, $I$ represents the moment of inertia.
• What theorem applies to the relationship between work and change in rotational kinetic energy?

  Work-energy theorem
• According to the work-energy theorem, the change in rotational kinetic energy is equal to the work done, which is expressed as $\tau \theta =$$\frac{1}{2} I (\omega_{f}^{2} - \omega_{i}^{2})$.theorem.
• What is torque defined as in rotational motion?

  Rotational force
• What is the formula for work done in terms of force, displacement, and angle?

  W = F \cdot d \cdot \cos \theta</latex>
• What does the formula $\tau =$$I \alpha$ demonstrate about the relationship between torque and angular acceleration?


  Directly proportional
• The work-energy theorem states that the work done on an object equals the change in its kinetic
• What is the formula that relates work and change in rotational kinetic energy according to the work-energy theorem?

  $W =$$\Delta KE_{rot}$
• What is the final angular velocity of a wheel with $I =$$3$ kg·m², starting at 2 rad/s, when a torque of 12 Nm is applied over an angular displacement of 4 radians?


  6 rad/s
• Positive torque rotates an object in a counterclockwise
• What is the first step in applying torque and work principles to rotating systems?

  Identify the System
• A pulley with $I =$$0.5$ kg·m² is spun by a motor applying 5 Nm of torque over 2 radians. If it starts from rest, what is its final angular velocity?


  6.32 rad/s
• What is torque defined as?

  Rotational force
• What does the magnitude of torque depend on?

  Force, distance, angle
• What is work defined as in physics?

  Force times displacement