---
title: "Engine crank 1800 rpm, connecting rod velocity"
subject: "Applied Mechanics (Dynamics)"
chapter: 4
key: "semester_3/applied_mechanics_dynamics:engine-crank-1800rpm-rod-velocity"
source: https://www.bctengineer.com/q/semester_3/applied_mechanics_dynamics/engine-crank-1800rpm-rod-velocity
site: BCT Engineering
---

# Engine crank 1800 rpm, connecting rod velocity

Applied Mechanics (Dynamics) · Chapter 4: Kinematics of Rigid Bodies

- Asked in: 2075 Chaitra, 2+8 marks
- Video: [D02L09 NUMERICAL 2/4  ENGINE FORCE ANALYSIS || GAGAN BANSAL](https://www.youtube.com/watch?v=FmEa1b-iujI) — GAGAN BANSAL
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/applied_mechanics_dynamics/engine-crank-1800rpm-rod-velocity
- Whole chapter: https://www.bctengineer.com/md/semester_3/applied_mechanics_dynamics/chapter-4

## Question

Define centre of rotation. In an engine system as shown in the figure below, crank AB has a constant clockwise angular velocity of 1800 rpm. For the crank position as shown, determine (a) the angular velocity of the connecting rod BD and (b) the velocity of the piston P. [Figure: crank AB (3 inch) at $40^\circ$ to the horizontal, connecting rod BD (8 inch), piston P at D.]

## Short answer

The instantaneous centre of rotation is a point (on the body or its extension) with zero velocity. Using v_B = omega_AB * AB and relative velocity, angular velocity of BD is 55.79 rad/s counter-clockwise; piston velocity v_D = 471.08 in/s (39.26 ft/s) to the right.

## Answer

**Instantaneous centre of rotation (ICR)** is the point in the plane of motion (on the body or on its imaginary extension) whose velocity is zero at that instant. At that instant the body behaves as if it were rotating about this point, so every point has speed $v = \omega\,r$, where $r$ is its distance from the ICR, and its velocity is perpendicular to the line joining it to the ICR.

#### Geometry
Take $A$ as origin, $x$ horizontal towards the piston, $y$ upward. The crank turns clockwise, so $\omega_{AB} = -188.50$ rad/s ($1800$ rpm $= 1800\times 2\pi/60$). The piston $D$ moves only horizontally, so $y_D = 0$:

$$
\sin\beta = \frac{AB\sin 40^\circ}{BD} = \frac{3\sin 40^\circ}{8} = 0.2410 \;\Rightarrow\; \beta = 13.95^\circ
$$

$$
\vec r_{B/A} = (2.2981\,\hat i + 1.9284\,\hat j)\ \text{in}, \qquad \vec r_{D/B} = (7.7641\,\hat i - 1.9284\,\hat j)\ \text{in}
$$

#### Velocities
Crank pin $B$ moves on a circle about $A$:

$$
\vec v_B = \vec\omega_{AB}\times\vec r_{B/A} = (363.49\,\hat i -433.19\,\hat j)\ \text{in/s}, \qquad v_B = \omega_{AB}\,AB = 565.49\ \text{in/s}
$$

For the connecting rod, $\vec v_D = \vec v_B + \omega_{BD}\hat k\times\vec r_{D/B}$ with $\vec v_D = v_D\hat i$:

$$
\begin{aligned}
\hat j:&\quad 0 = -433.19 + \omega_{BD}(7.7641) \;\Rightarrow\; \omega_{BD} = 55.79\ \text{rad/s}\\
\hat i:&\quad v_D = 363.49 + \omega_{BD}(1.9284) = 471.08\ \text{in/s}
\end{aligned}
$$

The positive $\omega_{BD}$ means the rod turns counter-clockwise.

**Answer: (a) $\omega_{BD} \approx 55.79$ rad/s counter-clockwise; (b) $v_P = v_D \approx 471.08$ in/s $= 39.26$ ft/s (to the right).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the instantaneous centre of rotation of a body in plane motion?
   A. The centre of mass of the body
   B. The point whose velocity is zero at that instant, about which the body appears to rotate
   C. The point with maximum acceleration
   D. The fixed pivot of the crank
   Answer: B. The ICR is the point (on the body or its extension) with zero velocity at that instant, so v = w r from it. (Key point: Instantaneous centre)

2. What is the crank angular velocity w_AB for 1800 rpm?
   A. 1800 rad/s
   B. 188.5 rad/s
   C. 30 rad/s
   D. 56.5 rad/s
   Answer: B. w = 1800 x 2 pi / 60 = 188.5 rad/s (clockwise). (Key point: Crank speed)

3. Which condition lets us find w_BD from vD = vB + w_BD k x rD/B?
   A. vD has no x component
   B. The piston moves only horizontally, so the j component of vD is zero
   C. The rod is at rest
   D. vB is zero
   Answer: B. Setting the vertical component of vD to zero gives 0 = -433.19 + w_BD(7.7641), so w_BD = 55.79 rad/s. (Key point: Piston constraint)

4. What is the piston velocity?
   A. 565.49 in/s
   B. 471.08 in/s (39.26 ft/s) to the right
   C. 363.49 in/s
   D. 55.79 in/s
   Answer: B. vD = 363.49 + 55.79(1.9284) = 471.08 in/s, which is 39.26 ft/s. (Key point: Piston velocity)

## Related in Applied Mechanics (Dynamics)

- [Engine crank 200 rpm, rod and piston acceleration](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Aengine-crank-200rpm-acceleration) — Applied Mechanics (Dynamics), chapter 4
- [Engine crank 2000 rpm, ICR, piston acceleration](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Aengine-crank-2000rpm-acceleration-icr) — Applied Mechanics (Dynamics), chapter 4
- [Coriolis meaning; engine crank 2000 rpm](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Aengine-crank-2000rpm-coriolis) — Applied Mechanics (Dynamics), chapter 4
- [Crank AB 5 rad/s, piston velocity](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Acrank-5rads-piston-velocity-coriolis) — Applied Mechanics (Dynamics), chapter 4
- [Coriolis acceleration; rod AB and BD velocity](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Acoriolis-define-rod-ab-bd-velocity) — Applied Mechanics (Dynamics), chapter 4
- [ICR; angular velocity of bar BD](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Aicr-bar-ab-bd-inches) — Applied Mechanics (Dynamics), chapter 4

## Related in other subjects

- [Slider crank velocity by instantaneous centre method](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Aslider-crank-velocity-instantaneous-centre) — Theory of Mechanism and Machine I, chapter 7
- [Velocity analysis of slider-crank mechanism](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_mechanics%3Acrank-slider-velocity-numerical) — Engineering Mechanics, chapter 5
- [Piston effort and crank-pin turning moment](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Aengine-piston-effort-turning-moment) — Theory of Mechanism and Machine II, chapter 1
- [Piston velocity and acceleration, equivalent system](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Apiston-velocity-acceleration-derivation) — Theory of Mechanism and Machine II, chapter 1