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Planar Kinematics of a Rigid Body
Multiple Choice

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/s2, 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/s2, 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/s2, 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 pin-connected at its midpoint and end points and has a length of 4 ft. 



10 .      

The 2-m-long 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 vc = 4 ft/s and deceleration of ac = 3 ft/s2 as shown. 



21 .      

The pulley os pin-connected 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/s2 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 rc = 0.2 ft and rd = 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/s2. Determine the angular velocity and angular acceleration of the dump bucket at this instant. 



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