AP Physics C: Mechanics Practice Quiz: Torque

Correct Answer: B

The provided content explicitly states that 'The torque exerted on a rigid system about a chosen pivot point by a given force is described by $\vec{\tau}=\vec{r}\times\vec{F}$'.

Correct Answer: C

The content specifies that 'The cross product between two vectors, $\vec{A}$ and $\vec{B}$, results in a vector quantity of magnitude $|\vec{A}\times\vec{B}|=AB\sin\theta$'.

Correct Answer: D

The content states that the direction of the vector resulting from a cross product is 'perpendicular to both vectors... and therefore is normal to the plane defined by' them. Since $\vec{r}$ and $\vec{F}$ define the xy-plane, the torque vector $\vec{\tau}$ must be normal (perpendicular) to it.

Correct Answer: B

The magnitude of the torque is given by $|\vec{\tau}|=rF\sin\theta$. The sine function, $\sin\theta$, has a maximum value of 1 when the angle $\theta$ is 90 degrees. Therefore, the torque is maximized when the force is applied perpendicular to the position vector.

Correct Answer: C

The magnitude of torque is $|\vec{\tau}|=rF\sin\theta$. If the force's line of action passes through the pivot point P, the angle $\theta$ between the position vector $\vec{r}$ and the force vector $\vec{F}$ is 0 or 180 degrees. Since $\sin(0^{\circ})$ and $\sin(180^{\circ})$ are both zero, the torque is zero.

Correct Answer: B

The provided content states that 'The cross product between two vectors... results in a vector quantity'. Since torque is defined as $\vec{\tau}=\vec{r}\times\vec{F}$, it is a vector quantity.

Correct Answer: D

The content explicitly states that 'The direction of the vector resulting from the cross-product... is perpendicular to both vectors $\vec{A}$ and $\vec{B}$ and therefore is normal to the plane defined by' them. Thus, $\vec{\tau}$ is perpendicular to the plane defined by $\vec{r}$ and $\vec{F}$.

Correct Answer: C

The definition of torque is given with respect to a chosen pivot point. The vector $\vec{r}$ is the position vector that originates at this pivot point and ends at the location where the force $\vec{F}$ is exerted on the rigid system.

Correct Answer: C

To identify and describe torques, one must use the defining equation $\vec{\tau}=\vec{r}\times\vec{F}$. This requires knowing the force vector ($\vec{F}$) and the position vector ($\vec{r}$) for each force.

Correct Answer: C

The content states that the resulting vector 'is perpendicular to both vectors $\vec{A}$ and $\vec{B}$ and therefore is normal to the plane defined by vectors $\vec{A}$ and $\vec{B}$'. In geometry, 'normal' is a synonym for 'perpendicular' when referring to a line and a plane.

Correct Answer: B

The magnitude of the torque is calculated using the formula $|\vec{\tau}| = rF\sin\theta$. Given that $\theta = 30^{\circ}$, and knowing that $\sin(30^{\circ}) = 0.5$, the magnitude of the torque is $rF(0.5) = 0.5rF$.

Correct Answer: B

The first point of the provided content is to 'Identify the torques exerted on a rigid system,' making this a primary skill or task in the context of this topic.

Correct Answer: C

Both $\vec{r}$ and $\vec{F}$ lie in the xy-plane because their z-components are zero. Based on the rule that the result of a cross product is 'normal to the plane defined by' the two vectors, the torque vector $\vec{\tau}$ must be normal to the xy-plane. The axis normal to the xy-plane is the z-axis.

Correct Answer: C

Torque is defined as a vector quantity, $\vec{\tau}$. The content specifies that a cross product results in a 'vector quantity' which has both magnitude ($AB\sin\theta$) and a specific direction (perpendicular to the plane of the two vectors). Therefore, a full description requires both magnitude and direction.