
1 . 

Gear A is in mesh with gear B as shown. If A starts from rest and has a constant angular acceleration of _{}_{A} = 2 rad/s^{2}, determine the tome needed for B to attain an angular velocity of _{B} = 50 rad/s.


2 . 

During a gust of wind, the blades of the windmill are given an angular acceleration of _{} = (0.2 _{} ) rad/s^{2}, where _{} is measured in radians. If initially the blades have an angular velocity of 5 rad/s, determine the speed of point P located at the tip of one of the blades just after the blade has turned two revolutions.


3 . 

Arm ABCD is printed at B and undergoes reciprocating motion such that _{} = (0.3 sin 4t) rad, where t is measured in seconds and the argument for the sine is in radiaus. Determine the largest speed of point A during the motion and the magnitude of the acceleration of point D at this instant.


4 . 

At the instant shown, gear A is rotating with a constant angular velocity of _{A} = 6 rad/s. Determine the largest angular velocity of gear B and the maximum speed of point C.


5 . 

The sphere starts from rest at _{} = 0 and rotates with an angular acceleration of _{} = (4_{}) rad/s^{2}, where _{} is measured in radians. Determine the magnitudes of the velocity and acceleration of point P on the sphere at the instant _{} = 6 rad.


6 . 

The mechanism is used to convert the constant circular motion of rod AB into translating motion of rod CD. Compute the velocity and acceleration of CD for any angle _{} of AB.


7 . 

Rod CD presses against AB, giving it an angular velocity. If the angular velocity of AB is maintained at = 5 rad/s, determine the required speed v of CD for any angle _{} of rod AB.


8 . 

The safe is transported on a platform which rests on rollers, each having a radius r. If the rollers do not slip, determine their angular velocity if the safe moves forward with a velocity v.


9 . 

The scaffold S is raised hydraulically by moving the roller at A towards the pin at B. If A is approaching B with a speed of 1.5 ft/s, determine the speed at which the platform is rising as a function of _{}. Each link is pinconnected at its midpoint and end points and has a length of 4 ft.


10 . 

The 2mlong bar is confined to move in the horizontal and vertical slots A and B. If the velocity of the slider block at A is 6 m/s, determine the bar's angular velocity and the velocity of block B at the instant _{} = 60°.


11 . 

Due to an engine failure, the missile is rotating at = 3 rad/s, while its mass center G is moving upward at 200 ft/s. Determine the magnitude of the velocity of its nose B at this instant.


12 . 

If the block at C is moving downward at 4 ft/s, determine the angular velocity of bar AB at the instant shown.


13 . 

Knowing the angular velocity of link CD is _{CD} = 4 rad/s, determine the angular velocities of links BC and AB at the instant shown.


14 . 

If rod CD has a downward velocity of 6in/s at the instant shown, determine the velocity of the gear rack A at this instant. The rod is pinned at C to gear B.


15 . 

The rotation of link AB creates an oscillating movement of gear F. If AB has an angular velocity of _{AB} = 8 rad/s, determine the angular velocity of gear F at the instant shown. Gear E is a part of arm CD and pinned at D to a fixed point.


16 . 

The automobile with wheels 2.5 ft in diameter is traveling in a straight path at a rate of 60 ft/s. If no slipping occurs, determine the angular velocity of one of the rear wheels and the velocity of the fastest moving point on the wheel.


17 . 

As the cord unravels from the wheel's inner hub, the wheel is rotating at = 2 rad/s at the instant shown. Determine the magnitudes of the velocities of point A and B.


18 . 

If the rim of the wheel and its hub maintain contact with the three stationary tracks as the wheel rolls, it is neccessary that slipping occurs at the hub A if no slipping occurs at B. Under these conditions, what is the speed at A if the wheel has an angular velocity ?


19 . 

The oil pumping unit consists of a walking beam AB, connecting rod BC, and crank CD. If the crank rotates at a constant rate of 6 rad/s, determine the speed of the rod hanger H at the instant shown. [Hint]


20 . 

Determine the angular acceleration of link BC at the instant _{} = 90° if the collar C has an instantaneous velocity of v_{c} = 4 ft/s and deceleration of a_{c} = 3 ft/s^{2} as shown.


21 . 

The pulley os pinconnected to block B at A. As cord CF unwinds from the inner hub with the motion shown, cord DE unwinds from the outer rim. Determine the angular acceleration of the pulley at the instant shown.


22 . 

The disk rolls without slipping such that it has an angular acceleration of _{} = 4 rad/s^{2} and angular velocity of = 2 rad/s at the instant shown. Determine the accelerations of points A and B on the link and the link's angular acceleration at this instant. Assume point A lies on the periphery of the disk, 150 mm from C.


23 . 

Gear C is rotating with a constant angular velocity of _{c} = 3 rad/s. Determine the acceleration of the piston A and the angular acceleration of rod AB at the instant _{} = 90°. Set r_{c} = 0.2 ft and r_{d} = 0.3 ft.


24 . 

At the instant shown, arm AB has an angular velocity of _{AB} = 0.5 rad/s and an angular acceleration of _{}_{AB} 2rad/s^{2}. Determine the angular velocity and angular acceleration of the dump bucket at this instant.


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