Torque and Cross Product of Vectors

Which of the following factors does NOT directly influence the torque produced by a force?

• Magnitude of the force

• Distance from the axis of rotation

• Mass of the object

• Angle at which the force is applied

A 50 N force is applied at the end of a 0.5 m wrench at an angle of 45° relative to the wrench. What would happen to the torque if the angle were increased to 90° while keeping all other variables constant?

• Torque would double

• Torque would remain the same

• Torque would increase by a factor of square root of 2

• Torque would decrease

Given three forces acting at different points along a lever, which of the following methods would best determine the resultant torque about the axis of rotation?

• Sum of the magnitudes of each force

• Calculate each individual torque, assign signs, and then get the sum of the torques

• Take the vector product of all three forces

• Sum the distances of each force from the axis and multiply by the net force

A 10 N force is applied at an angle to a 1 m lever arm. If the force is applied at 60° to the arm, what is the torque?

• 5 Nm

• 8.66 Nm

• 10 Nm

• 15 Nm

A force is applied to a wrench perpendicular to the handle at a distance r from the axis of rotation. Explain how the torque will change if the distance is halved while keeping the force constant.

• Torque doubles

• Torque is halved

• Torque remains constant

• Torque decreases to one-quarter

What is the significance of the sign convention in torque calculations, and how does it affect the analysis of rotational systems?

• Positive and negative signs indicate the magnitude of force.

• The sign convention differentiates direction (clockwise vs. counterclockwise), helping to determine resultant torque.

• It indicates if the force vector is applied upward or downward.

• It is used to calculate only the distance component of torque.

Given a vector force F = 3i + 4j and position vector r=2i−3j, what is the magnitude of the torque generated by these vectors?

• 0

• 6

• 17

• 22

A wrench applies a torque of 15 Nm to a bolt. If the applied force is increased by 50% and the distance from the axis remains the same, what is the new torque?

• 7.5 Nm

• 15 Nm

• 22.5 Nm

• 30 Nm

Two forces of equal magnitude act at two points equidistant from the pivot, one clockwise and one counterclockwise. What can we conclude about the resultant torque?

• The resultant torque is positive.

• The resultant torque is negative.

• The resultant torque is zero.

• The system rotates counterclockwise.

If the length of a wrench is doubled, and the force applied remains constant, by what factor does the torque increase?

• 0.5

• 1

• 2

• 4