Chapter 12: Q.40 (page 332)

Force $\vec{F} = - 10 \hat{ȷ} N$ is exerted on a particle at $\vec{r} = (5 \hat{ı} + 5 \hat{ȷ}) m$ . What is the torque on the particle about the origin?

Short Answer

Expert verified

The particle's torque around the origin is $- (50 N \cdot m) \hat{k}$ .

Step by step solution

Formula for torque

Another technique to combine two vectors is to use the vector or cross product, which produces a vector that is perpendicular to both of the originals.

Torque is the cross product of the radius vector (from the axis of rotation to the site of force application) and the force vector in vector form.

$T = r \times F$

$T$ is torque.

$F$ is force.

Calculation of Torque

The torque on the particle of origin

$r \times F = |\begin{array}{ccc} i & j & k \\ 5 m & 5 m & 0 m \\ 0 N & - 10 N & 0 N \end{array}|$

$= i (0) - j (0) + k ((5 m) (- 10 N) - 0 N \cdot m)$

= - k (50 N - m)

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Force $\vec{F} = - 10 \hat{ȷ} N$ is exerted on a particle at $\vec{r} = (5 \hat{ı} + 5 \hat{ȷ}) m$ . What is the torque on the particle about the origin?

Short Answer

Step by step solution

Formula for torque

Calculation of Torque

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Force F→=−10ȷ^Nis exerted on a particle at r→=(5ı^+5ȷ^)m. What is the torque on the particle about the origin?

Short Answer

Step by step solution

Formula for torque

Calculation of Torque

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Atoms and Radioactivity

Magnetism

Physical Quantities And Units

Fundamentals of Physics

Space Physics

Study anywhere. Anytime. Across all devices.

Force $\vec{F} = - 10 \hat{ȷ} N$ is exerted on a particle at $\vec{r} = (5 \hat{ı} + 5 \hat{ȷ}) m$ . What is the torque on the particle about the origin?