6.4.2 Newton's Second Law for Rotational Motion

Question 1

Newton’s Second Law for Rotational Motion

Answer 1

• Newton’s second law for rotational motion is . This is the rotational analogue of .
• The equation can be derived by considering a simple rigid body to which a torque is applied. The torque has an associated tangential force, which causes linear acceleration via .
• In general, there is more than one torque in a given situation:

Question 2

Assume that a rigid body is attached to the end of a massless string of length r, and that the body’s other end can rotate freely about a pivot. The moment of inertia of the rigid body ____________.

Answer 2

• depends on the axis of rotation
• cannot be zero
• depends on the mass distribution

Question 3

Consider very small contiguos masses m1, m2, … , mn, that equal M, the total mass of an object. Also consider that I, the moment of intertia of the object, is equal to sigma i delta Ii. The moment of intertia of such an object _______________

Answer 3

depends not only on its total mass and mass distribution, but also on the orientation and position of the axis of rotation.

Question 4

Four particles of mass m are connected by massless rods to form a rectangle of sides 2a and 2b. What is the moment of inertia of this system?

Answer 4

8ma^ 2

Question 5

Consider a mass m connected to a rod that is free to rotate around a pivot point. Which of the following is not correct?

Answer 5

The radial component of the force results in a greater torque for a given acceleration.

Question 6

Which of the following statements about the moment of inertia is not correct?

Answer 6

A rigid body rotated around different axes of rotation has the same moment of inertia.

Question 7

A student opens a 15.00 kg door by applying a constant force of 40.00 N from a perpendicular distance of 0.90 m from the hinges. If the door is 2.00 m in height and 1.20 m wide, what is the magnitude of the angular acceleration of the door? Assume that the door rotates freely on its hinges.

Answer 7

5.00 rad / s^2

Question 8

Which of the following is not correct?

Answer 8

An object with most of its moment of inertia located near the axis of rotation has a larger moment of inertia than an object of the same mass with most of its mass located far from the axis of rotation.

Question 9

In pure rotational motion of a rigid body, ______________________.

Answer 9

all the particles of the body have the same angular velocity

Question 10

Four particles each of mass m are connected by massless rods to form a rectangle of sides 2a and 2b. The system rotates about an axis through its center and parallel to the plane of the figure. What is the moment of inertia about the axis?

Answer 10

4ma^2