Ch1_Rotational Dynamics_Test1

What is the relationship between torque and angular acceleration?

• Torque is directly proportional to angular acceleration.

• Torque and angular acceleration are unrelated.

• Torque is inversely proportional to angular acceleration.

• Torque has no effect on angular acceleration.

Answer explanation

Torque is directly proportional to angular acceleration, as described by Newton's second law for rotation: τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.

Define moment of inertia and its significance in rotational motion.

• Moment of inertia is a measure of an object's resistance to changes in its rotational motion, significant for calculating angular acceleration in response to applied torque.

• Moment of inertia is the same as mass in linear motion.

• Moment of inertia has no effect on the speed of rotation.

• Moment of inertia only applies to solid objects, not fluids.

Answer explanation

The correct choice defines moment of inertia as an object's resistance to changes in rotational motion, crucial for determining angular acceleration when torque is applied, highlighting its significance in dynamics.

How is rotational kinetic energy calculated for a rotating object?

• KE_rot = I * ω

• KE_rot = 0.5 * I * ω²

• KE_rot = 0.5 * m * v²

• KE_rot = I * ω

Answer explanation

Rotational kinetic energy is calculated using the formula KE_rot = 0.5 * I * ω², where I is the moment of inertia and ω is the angular velocity. This shows that the energy depends on both the inertia and the square of the rotation speed.

State the principle of conservation of angular momentum.

• External torques are necessary for angular momentum to remain constant.

• The total angular momentum of a closed system remains constant if no external torques act on it.

• The total angular momentum of a system always increases over time.

• Angular momentum can be created or destroyed in a closed system.

Answer explanation

The correct choice states that the total angular momentum of a closed system remains constant if no external torques act on it. This reflects the principle of conservation of angular momentum, which is fundamental in physics.

What factors affect the rolling motion of an object?

• Mass, shape, size, surface texture, incline, friction, and moment of inertia.

• Color, weight, temperature, and sound

• Material density, air pressure, and humidity

• Speed, acceleration, and gravitational pull

Answer explanation

The correct choice includes factors like mass, shape, size, surface texture, incline, friction, and moment of inertia, all of which directly influence the rolling motion of an object. Other options do not relate to rolling motion.

Explain the characteristics of uniform circular motion.

• Characteristics of uniform circular motion include constant speed, changing velocity, net centripetal force, and uniform angular velocity.

• Variable speed with no net force

• Centrifugal force acting outward

• Constant acceleration in a straight line

Answer explanation

Uniform circular motion is characterized by constant speed and uniform angular velocity, but the velocity vector changes direction, requiring a net centripetal force. The other options do not accurately describe this motion.

What is the radius of gyration and how is it calculated?

• The radius of gyration is calculated as k = I/m.

• The radius of gyration is a measure of mass density.

• The radius of gyration is determined by the shape of the object.

• The radius of gyration is calculated using the formula k = sqrt(I/m).

Answer explanation

The radius of gyration (k) is calculated using the formula k = sqrt(I/m), where I is the moment of inertia and m is the mass. This formula highlights the relationship between mass distribution and rotational inertia.

Describe the parallel axes theorem and its application.

• The parallel axes theorem relates the moment of inertia of a body about any axis to its moment of inertia about a parallel axis through its center of mass.

• It describes the relationship between mass and velocity in linear motion.

• The theorem applies only to circular objects and their rotation.

• The parallel axes theorem states that the moment of inertia is constant regardless of the axis.

Answer explanation

The correct choice explains the parallel axes theorem, which connects the moment of inertia about any axis to that about a parallel axis through the center of mass, highlighting its importance in rotational dynamics.

What is the perpendicular axes theorem and when is it used?

• It is used to calculate the mass of three-dimensional objects.

• The theorem states that the moment of inertia is the same about any axis.

• The theorem applies only to solid spheres and cylinders.

• The perpendicular axes theorem relates the moment of inertia of a planar object about a perpendicular axis to the sum of its moments of inertia about two axes in its plane.

Answer explanation

The perpendicular axes theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two axes in its plane, making it essential for planar objects.

How does torque influence the rotational motion of an object?

• Torque influences rotational motion by determining the angular acceleration of an object.

• Torque is irrelevant to the direction of rotation.

• Torque has no effect on linear motion.

• Torque only affects the speed of an object.

Answer explanation

Torque is crucial in rotational motion as it determines the angular acceleration of an object, directly influencing how quickly it spins. The correct choice highlights this fundamental relationship.