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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

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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

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Problem # 3:

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

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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

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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

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Problem # 6:

The position of a particle is defined by

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Problem # 7:

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

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Problem # 8:

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

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Problem # 9:

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

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Problem # A-1:

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

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Problem # A-2:

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

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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

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Problem # A-4:

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

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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

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Problem # A-6:

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

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Problem # A-7:

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

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Problem # B-1:

If link CD is rotating at

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Problem # B-2:

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

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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.

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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.

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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.

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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.

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Problem # B-7:

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

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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

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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

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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.

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Problem # C-4:

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

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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?

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Problem # C-6:

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

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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.

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Problem # D-2:

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

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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.

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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.

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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.

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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

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Problem # D-7:

A crank OA rotates counterclockwise at an angular velocity

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Problem # D-8:

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

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Problem # E-1:

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

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Problem # E-2:

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

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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

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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

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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

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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

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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

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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

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Problem # E-9:

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

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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.

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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

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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

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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

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Problem # E-14:

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

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Problem # E-15:

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

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Problem # E-16:

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

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