One force acting on a machine part is F=(-5.00 N) + (4.00 N) . The vector from the origin to t

step 1 Hi everyone this is the problem based on torque due to the force on a body here it is given forc

One force acting on a machine part is F=(-5.00 N) + (4.00...

One force acting on a machine part is $\overrightarrow{\boldsymbol{F}}=(-5.00 \mathrm{~N}) \hat{\imath}+$ $(4.00 \mathrm{~N}) \hat{\jmath}$. The vector from the origin to the point where the force is applied is $\overrightarrow{\boldsymbol{r}}=(-0.450 \mathrm{~m}) \hat{\imath}+(0.150 \mathrm{~m}) \hat{\jmath}$. (a) In a sketch, show $\overrightarrow{\boldsymbol{r}}, \overrightarrow{\boldsymbol{F}},$ and the origin. (b) Use the right-hand rule to determine the direction of the torque. (c) Calculate the vector torque for an axis at the origin produced by this force. Verify that the direction of the torque is the same as you obtained in part ( $(\mathrm{b})$.

One force acting on a machine part is $\overrightarrow{\boldsymbol{F}}=(-5.00 \mathrm{~N}) \hat{\imath}+$
$(4.00 \mathrm{~N}) \hat{\jmath}$. The vector from the origin to the point where the force is applied is $\overrightarrow{\boldsymbol{r}}=(-0.450 \mathrm{~m}) \hat{\imath}+(0.150 \mathrm{~m}) \hat{\jmath}$. (a) In a sketch, show $\overrightarrow{\boldsymbol{r}}, \overrightarrow{\boldsymbol{F}},$
and the origin. (b) Use the right-hand rule to determine the direction of the torque. (c) Calculate the vector torque for an axis at the origin produced by this force. Verify that the direction of the torque is the same as you obtained in part ( $(\mathrm{b})$.

Key Concepts

Torque

Torque is a measure of the rotational effect produced by a force applied at a distance from an axis of rotation. It is defined mathematically as the cross product of the position vector (the vector from the axis of rotation to the point of force application) and the force vector. The magnitude of the torque depends on the size of the force, the distance from the axis, and the angle between the force and the position vector.

Vector Cross Product

The vector cross product is an operation on two vectors in three-dimensional space that results in a new vector. This vector is perpendicular to the plane formed by the original two vectors, and its magnitude is given by the product of the magnitudes of the two vectors and the sine of the angle between them. It is commonly used in physics to calculate torque and angular momentum.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the vector resulting from a cross product. In the context of torque, you point the fingers of your right hand in the direction of the position vector, then curl them towards the force vector; your thumb will then point in the direction of the torque vector. This rule helps visualize and confirm the orientation of the calculated torque.

Force and Position Vectors

Force and position vectors are fundamental in mechanics, representing the magnitude and direction of a force acting on a body and the location at which the force is applied, respectively. The interaction between these vectors, through operations like the cross product, helps determine quantities such as torque, enabling the analysis of rotational dynamics in physical systems.

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