physics tests, Physics1

Review Problems

(Related to chapters 10, 11, 12, 13)

1. Four equal masses are located at the corners of a square of side connected by essentially massless rods. Find the moment of

inertia of this system about an axis a) that coincides with one side and (b) that bisects two opposite sides.

2. Moment of inertia of a uniform thin rod of mass M and length L about an axis through its center and perpendicular to its length is

. Find its moment of inertia through through an axis passing through one of its ends and perpendicular to its length.

3. A 1.10-kg wrench is acting on a nut trying to turn it. The length of the wrench lies directly to the east of the nut. A force 15.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0◦ north of east. What is the magnitude of the torque about the center of the nut?

4. A uniform disk of mass M kg and radius R cm is mounted on a fixed horizontal axle. A block with mass m kg hangs from a massless cord that is wrapped around the rim of the disk. Find the acceleration of the block, angular acceleration of the disk, and the tension in the cord. The cord does not slip, and there is no friction at the axle.

m L

[Ans : 2mL2, mL2]

ML2 /12

[Ans : ML2

3 ]

[1.125 Nm]

5. A 3.0-m-diameter merry-go-round with rotational inertia 120 kg. m2 is spinning freely at 0.50 rev/s. Four 25-kg children sit suddenly on the edge of the merry-go-round. (a) Find the new angular speed, and (b) determine the total energy lost to friction between children and merry- go-round. [Ans : (a)1.09 rad/s,(b)386 J]

6. A uniform beam of length and mass is at rest with its ends on the two pivots. The pivot at the right end exerts a force on the beam. Where should a person of mass sit for the beam to be in static

equilibrium?

7. A block of is hanging to a vertical spring of spring constant . If the spring is stretched additionally from the new equilibrium, find the time period of oscillations.

L M F

m

[Ans : (FL − Mg L2 )

mg ]

m k

[Ans : T = 2π m /k]

4. A projectile is fired vertically from Earths surface with an initial speed of 10 km/s. Neglecting air drag, how far above the surface of earth will it go? (Mean radius of the Earth=6.38⇥106 m, G = 6.67⇥10�11 Nm2/kg2, Mass of the Earth = 5.97⇥ 1024 kg)

5. A 20-g bullet traveling 200 m/s penetrates a 2.0-kg block of wood and emerges going 150 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?

6. A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together. Assume that any other unbalanced forces are negligible. (a) What is the speed of the wreckage just after the collision? (b) In what direction does the wreckage move just after the collision?

7. A 1.10-kg wrench is acting on a nut trying to turn it. The length of the wrench lies directly to the east of the nut. A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0� north of east. What is the magnitude of the torque about the center of the nut?

8. Four equal masses m are located at the corners of a square of side L connected by essentially massless rods. Find the moment of inertia of this system about an axis a) that coincides with one side and (b) that bisects two opposite sides.

9. Moment of inertia of a uniform thin rod of mass M and length L about an axis through its center and perpendicular to its length is ML

2

12 . Find its moment of inertia through through an axis passing through one of its ends and perpendicular to its length.

10. A uniform disk of mass M=3.5 kg and radius R=25 cm is mounted on a fixed horizontal axle. A block with mass m=1.5 kg hangs from a massless cord that is wrapped around the rim of the disk. Find the acceleration of the block, angular acceleration of the disk, and the tension in the cord. The cord does not slip, and there is no friction at the axle.

M

m

2

[An s : g

1 + M2m ,

1 R

g

1 + M2m ,

M 2

g

1 + M2m ]

8. A uniform thin rod of mass and length is suspended from a pivot point as shown below. Find the period of oscillations of this rod.

M L

L/5 pivot