The example problems are all uniquely numbered for easy reference. The problem statement is given, and then the solution is provided as a PDF file which you can download.

If you want to review the theory behind all these problems, I conveniently cover that on this website, in the kinematics and dynamics pages. Note that this page is a work in progress and new content will be added regularly (however, the kinematics sections are completed).

To see the example problems click on the category you are interested in:

Kinematics – Curvilinear motion problems involving normal and tangential components

Kinematics – Curvilinear motion problems involving radial and transverse components

Kinematics – Problems involving instant center

Kinematics – 2-D problems involving relative-motion analysis with rotating axes

Kinematics – 2-D problems involving relative-motion analysis with acceleration

Kinematics – 3-D problems involving general motion

Problem # 1:

A jet aircraft is flying along an arc, and at the instant shown it has a speed of 500 ft/s and an acceleration of 70 ft/s

Download solution

Problem # 2:

A jet aircraft flies along a vertical parabolic path, and at point P it has a speed of 260 m/s, which is increasing at a rate of 0.9 m/s

Download solution

Problem # 3:

At a certain instant, a car at A has a speed of 25 m/s and an acceleration of 12 m/s

Download solution

Problem # 4:

A car travels at a speed of 8 m/s along a circular road which has a radius of 60 m. Starting from

Download solution

Problem # 5:

A car travels at a speed of 8 m/s along a circular road which has a radius of 60 m. Starting from a time of

Download solution

Problem # 6:

The position of a particle is defined by

Download solution

Problem # 7:

A particle travels along a path such that its acceleration is defined by

Download solution

Problem # 8:

An arm rotates about a pivot O, and its end P speed increases according to the equation d

Download solution

Problem # 9:

A particle P is traveling along a circular arc of radius 5 m. The speed of the particle is given by

Download solution

Problem # A-1:

The rod OA is rotating in a horizontal plane about point O such that

Download solution

Problem # A-2:

A slotted link rotates about point O with a constant angular velocity d

Download solution

Problem # A-3:

A rod is rotating about a point O, while pushing a pin P along a circular slot, as shown. The pin P is also free to slide along a slot in the rod, as shown. If the rod rotates at constant rate d

Download solution

Problem # A-4:

For a short distance, a particle P travels along a path defined by

Download solution

Problem # A-5:

A robotic arm with end point P rotates about point O, while also changing its length such that the distance from point O to point P is given by

Download solution

Problem # A-6:

A rocket is launched vertically upward and at a given instant makes an angle of

Download solution

Problem # A-7:

A rocket is launched vertically upward and at a given instant makes an angle of

Download solution

Problem # B-1:

If link CD is rotating at

Download solution

Problem # B-2:

For the arrangement shown, determine the speed of block A.

Download solution

Problem # B-3:

A wheel rolls with slipping on a surface, and as a result, the top and bottom of the wheel have a velocity of 6 m/s and 1 m/s, respectively. Determine the velocity of the center C of the wheel.

Download solution

Problem # B-4:

A wheel rolls with slipping on a surface, and as a result, the top and bottom of the wheel have a velocity of 7 m/s and 2 m/s, respectively. Determine the velocity of the center C and point D on the wheel.

Download solution

Problem # B-5:

A wheel rolls with slipping on a surface, and as a result, the top and bottom of the wheel have a velocity of 9 ft/s and 6 ft/s, respectively. Determine the velocity of the center C and point D on the wheel.

Download solution

Problem # B-6:

In the assembly shown, A and B are collars which are free to slide along the vertical rod shown. The velocity of collar B is 520 mm/s in the downward direction. Calculate (a) the velocity of collar A, and (b) the angular velocity of link CD.

Download solution

Problem # B-7:

In the gear arrangement shown, the link AB has an angular velocity of

Download solution

Problem # C-1:

A block B is moving along a slot at a velocity of 3 m/s relative to the slot and at an acceleration of 5 m/s

Download solution

Problem # C-2:

A block B is moving along a rotating disk in the direction shown with a velocity of 3 ft/s and an acceleration of 5 ft/s

Download solution

Problem # C-3:

A rod in the shape of a circular arc rotates about A such that a pin pushing against the rod, as shown, is moving to the right at a constant speed of 85 mm/s. Determine the angular velocity and angular acceleration of the rod at the instant shown. Note that the pin is sliding along the rod.

Download solution

Problem # C-4:

In an amusement park ride, the main arm is rotating about A at a constant angular velocity of

Download solution

Problem # C-5:

A wheel is rolling as shown without slipping. The pin B on the wheel is pushing against and sliding along the rod which is free to pivot about point A. What is the angular velocity and angular acceleration of the rod?

Download solution

Problem # C-6:

In an amusement park ride, the main arm is rotating about A with an angular velocity of

Download solution

Problem # D-1:

At the instant shown, a wheel and rod mechanism is in motion with dimensions and angular motions as shown. Calculate the acceleration of the collar B at this instant.

Download solution

Problem # D-2:

For the linkage arrangement shown, what is the angular acceleration of links AB and BC at the instant shown.

Download solution

Problem # D-3:

In the arrangement shown, determine the angular velocity and angular acceleration of wheel 1, wheel 2, and link AC, at the instant shown.

Download solution

Problem # D-4:

At the instant shown, a cylinder is supported between two boards, and each board is moving with the velocity and acceleration shown. Determine the angular velocity and angular acceleration of the cylinder.

Download solution

Problem # D-5:

The rod AB has endpoints at A and B which are free to move in the groove shown. Calculate the angular velocity and angular acceleration of the rod at the instant shown.

Download solution

Problem # D-6:

A slotted carriage is free to slide back and forth using lubricated sleeves as support, as shown. A rotating link OP is the driver of this motion. The distance between O and P is

Download solution

Problem # D-7:

A crank OA rotates counterclockwise at an angular velocity

Download solution

Problem # D-8:

A wheel rolls without slipping on a flat surface with an angular velocity

Download solution

Problem # E-1:

A rod is rotating about the z-axis with an angular velocity

Download solution

Problem # E-2:

A rod is rotating about the z-axis with an angular velocity

Download solution

Problem # E-3:

A gyrotop is rotating as shown. The wheel on the end of the rod is being rotated with a motor which rotates with an angular velocity of

Download solution

Problem # E-4:

A wheel rolls along a level surface without slipping. The wheel rotates on a shaft, and the shaft rotates about point O with an angular velocity of

Download solution

Problem # E-5:

A wheel rolls along a level surface without slipping. The wheel is connected to a shaft which has a ball-and-socket joint at O, around which the shaft and wheel rotate, with a spin angular velocity of

Download solution

Problem # E-6:

A wheel rolls along a level surface without slipping. The wheel is connected to a shaft which has a ball-and-socket joint at O, around which the shaft and wheel rotate. The wheel and shaft precess around point O, with an angular velocity of

Download solution

Problem # E-7:

A cone rolls on the xz-plane without slipping, with its tip at the origin O, around which the cone rotates. The cone precesses around point O, with an angular velocity

Download solution

Problem # E-8:

A wheel rolls along a conical surface without slipping. The wheel is connected to a shaft which has a ball-and-socket at O, around which the shaft and wheel rotate. The wheel and shaft precess around point O, with an angular velocity of

Download solution

Problem # E-9:

In the gear system shown, gear 4 rotates with an angular velocity

Download solution

Problem # E-10:

The rod AB has ball-and-socket joints at both ends which are attached to smooth collars A and B. Determine the angular velocity of the rod, and the velocity and acceleration of collar B at the instant shown.

Download solution

Problem # E-11:

A rod AB is attached to a rotating disk at one end A with a ball-and-socket joint, and the other end B is attached to a clevis, which is attached to a collar that can slide along a vertical rod in the z-direction. The disk rotates in the xy-plane at a constant rate of

Download solution

Problem # E-12:

A rod AB and a rod CD are attached to a rotating disk with a ball-and-socket joint at one end. At the other end, rod AB is attached to a clevis, which is attached to a collar that can slide along a horizontal rod EF, in the y-direction. The other end of rod CD is attached to another collar with a ball-and-socket joint, and this collar can also slide along the rod EF. The disk rotates in the xy-plane at an angular velocity of

Download solution

Problem # E-13:

A rod AB and a rod CD are attached to a rotating disk with a ball-and-socket joint at one end. At the other end, rod AB is attached to a clevis, which is attached to a collar that can slide along a rod EF. The other end of rod CD is attached to another collar with a ball-and-socket joint, and this collar can also slide along the rod EF. The disk rotates in the xy-plane at an angular velocity of

Download solution

Problem # E-14:

A disk is rotating about the z-axis with an angular velocity of

Download solution

Problem # E-15:

A rectangular plate is rotating about the z-axis with an angular velocity of

Download solution

Problem # E-16:

A bar is rotating about the z-axis with an angular velocity of

Download solution

Return to

Return to