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Physics problems: dynamics

Rotation of a rigid body; torque

 

Problem 6.

A boy of mass 40 kg wishes to play on pivoted seesaw with his dog of mass 15 kg. When the dog sits at 3 m from the pivot, where must the boy sit if the 6.5 me long board is to be balanced horizontally?

Solution

 

Problem 10.

A uniform, solid metal disk of mass 6.0 kg and diameter 2.0 cm hangs in a horizontal plane, supported at its center by a vertical metal wire.  You find that it requires a horizontal force of 4 N tangent to the rim of the disk to turn it by 5 degrees, thus twisting the wire.  You now remove this force and release the disk from rest.

(a) What is the torsion constant for the metal wire? 

(b) Write the equation of motion for twist angle of the disk.

Solution

 

Problem 22.

A soccer ball of diameter 35 cm rolls without slipping at a linear speed of 2 m/s. Though how many revolutions has the soccer ball turned as it moves a linear distance of 20 m?

Solution

 

Problem 23.

A bicycle is moving at 10 m/s.  What is the angular speed of its tires if their radius is 30 cm?

Solution

 

 

 

 

 

Problem 43.

A 100 kg load is placed on a 40 kg stretcher to be carried by two persons. The stretcher is 2m long and the load is placed 0.6m from the left end. How much force must each person exert to carry the stretcher?

Solution

 

Problem 44.

A painter weighing 900 N stands on a massless plank 5 m long that is supported at each end by a stepladder. If he stands 1m from one end of the plank, what force is exerted by each stepladder?

Solution

 

Problem 45.

A 20 kg child and a 30 kg child sit at opposite ends of a 4 m seesaw that is pivoted at its center. Where should another 20 kg child sit in order to balance the seesaw?

Solution

 

Problem 51.

The moment of inertia of a 0.98-kg bicycle wheel rotating about its center is equation moment inertia. What is the radius of this wheel, assuming the weight of the spokes can be ignored?

Solution

 

Problem 59.

A meter stick tied at its center carries two 10 g weights. Where should 50 g weight be placed if the first 10 g weight is 10 cm away from the fulcrum and the second weight is placed 30 cm away from the fulcrum

Solution

 

Problem 62.

A uniform meter scale can be balanced at the 70 cm mark when a mass of 0.05 kg is hung from the 94 cm mark, draw a diagram of the arrangement, find the mass of the meter scale.

Solution

 

Problem 63.

A uniform meter scale of weight 50 g is balanced at 30 cm mark when weights of 80 g and 60 g act at 5 cm mark and 45 cm mark, respectively.  What force must be applied at 20 cm mark to balance the meter scale?

Solution

 

 

 

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