13. if you shorten the length of string by half that holds an object in rotation at the same tangential
speed, tension in the string

 remains unchanged.
 doubles.
 quadruples.
 is halved.
14. a revolution and a rotation are
 different terms of the same concept.
 different from each other with different units of measurement.
 variations of centripetal forces.
 variations of centrifugal forces.
15. for a rotating bicycle wheel, the spokes of the wheel all have the same
 linear speed.
 tangential speed.
 rotational speed.
 radial speed.

16. when you whirl a tin can overhead in a horizontal circle, the force that the can exerts on the
string acts in a direction
 toward the center of the path.
 away from the center of the path.
 either toward or away from the center.
 parallel to the force of gravity.
17. for a conical pendulum, the vertical component of string tension is equal to the
 weight of the bob.
 horizontal component of string tension.
 centripetal force.
 centrifugal force.
18. for a conical pendulum, the centripetal force is equal to the
 weight of the bob.
 tension in the string.
 vertical component of string tension.
 horizontal component of string tension.
19. a bug inside a can whirled in a circle feels a force of the can on its feet. this force acts in a
direction
 inward, toward the center of swing.

 outward, away from the center of swing.
 either inward or outward, toward or away from the center of swing.
 parallel to the force of gravity.
20. the normal force on a car executing a turn on a banked track does not depend on the
 angle of the bank.
 speed of the car.
 radius of curvature.
 friction between the tires and the road.

13. doubles

The tension in the string corresponds to the centripetal force that holds the object in rotation, so:

where m is the mass of the object, v is the tangential speed, and r is the distance of the object from the centre of rotation (therefore it corresponds to the length of the string). The problem tells us that the tangential speed remains the same (v), while the length of the string is halved, so r'=r/2. Therefore, the new tension in the string will be

so, the Tension doubles.

14. Variations of centripetal forces

Both revolution and rotation refer to the rotational motion of an object, therefore they both involve the presence of a centripetal force, which keeps the object in circular motion. The only difference between the two is:

- Revolution is the circular motion of an object around a point external to the object (for instance, the motion of the Earth around the Sun)

- Rotation is the circular motion of an object around its centre, so around a point internal to the object (for instance, the rotation of the Earth around its axis)

15. Rotational speed

For a uniform object in circular motion, all the points of the object have same rotational speed. In fact, the rotational speed is defined as

where is the angular displacement covered in a time interval of . Since all the points of the wheel are coeherent (they move together), they all cover the same angular displacement in the same time, so they all have same rotational speed.

16. away from the center of the path.

The tension in the string is responsible for keeping the tin can in circular motion. Therefore, the tension in the string represents the centripetal force, and so it is directed towards the centre of the path. According to Newton's third law, the tin can exerts a force on the string which is equal in magnitude (so, same magnitude of the tension), but opposite in direction: therefore, away from the centre of the path.

17. weight of the bob.

There are two forces acting on the bob in the vertical direction: the weight of the bob (downward) and the vertical component of the string tension (upward). Since there is no acceleration along the vertical direction, the net force must be zero, so these two forces must be equal: it means that the vertical component of the string tension is equal to the weight of the bob. Along the horizontal direction, instead, the horizontal component of the string tension corresponds to the centripetal force that keeps the bob in circular motion.

18. horizontal component of string tension.

Along the horizontal direction, there is only one force acting on the bob: the horizontal component of the string tension. Since the bob is moving of circular motion along the horizontal direction, this means that this force (the horizontal component of the string tension) must correspond to the centripetal force that keeps the pendulum in circular motion.

19. inward, toward the center of swing.

The force that the can exerts on the bug is the force that keeps the bug in circular motion (since it prevents the bug from moving away). Therefore, it must corresponds to the centripetal force.

20. speed of the car. AND radius of curvature.

The normal force exerted on a car executing a turn on a banked track is given by the expression:

where m is the mass of the car, g is the gravitational acceleration, is the angle of the bank, and is the coefficient of friction.

From the formula, we see that the normal force depends on (the angle of the bank) and (the coefficient of friction), while it does not depend on the speed of the car or on the radius of curvature. Therefore, these two are the correct answers.

because if the tool that you are using is not balanced it there would be false mass.