Unit 5: Torque and Rotational Dynamics

Question 1

What is torque?

Answer 1

Torque is a measure of the rotational force applied to an object.

Question 2

What is the formula for torque?

Answer 2

Torque (τ) = r × F × sin(θ), where r is the distance from the pivot point, F is the force, and θ is the angle between the force and the lever arm.

Question 3

True or False: Torque is a scalar quantity.

Answer 3

False; torque is a vector quantity.

Question 4

If the force is applied perpendicular to the lever arm, what is the maximum torque?

Answer 4

Maximum torque occurs when θ = 90 degrees, so τ = r × F.

Question 5

What unit is torque measured in?

Answer 5

Torque is measured in Newton-meters (Nm).

Question 6

What is rotational equilibrium?

Answer 6

Rotational equilibrium occurs when the net torque acting on an object is zero.

Question 7

What is the relationship between torque and angular acceleration?

Answer 7

The net torque acting on an object is equal to the product of its moment of inertia and its angular acceleration (τ = Iα).

Question 8

What does the moment of inertia depend on?

Answer 8

The moment of inertia depends on the mass of the object and the distribution of that mass relative to the axis of rotation.

Question 9

What is the formula for moment of inertia for a point mass?

Answer 9

Moment of inertia (I) = m × r², where m is the mass and r is the distance from the axis of rotation.

Question 10

What is the parallel axis theorem?

Answer 10

The parallel axis theorem states that I = I_cm + md², where I_cm is the moment of inertia about the center of mass, m is the mass, and d is the distance from the center of mass to the new axis.

Question 11

What is angular momentum?

Answer 11

Angular momentum (L) is the product of the moment of inertia and the angular velocity (L = Iω).

Question 12

What is the principle of conservation of angular momentum?

Answer 12

The principle states that in the absence of external torques, the total angular momentum of a system remains constant.

Question 13

What is the formula for angular velocity?

Answer 13

Angular velocity (ω) = Δθ / Δt, where Δθ is the change in angle and Δt is the change in time.

Question 14

True or False: Angular velocity is a scalar quantity.

Answer 14

False; angular velocity is a vector quantity.

Question 15

What is the relationship between linear velocity and angular velocity?

Answer 15

Linear velocity (v) = r × ω, where r is the radius and ω is the angular velocity.

Question 16

What is centripetal acceleration?

Answer 16

Centripetal acceleration (a_c) is the acceleration directed towards the center of a circular path, given by a_c = v² / r.

Question 17

What is the formula for gravitational torque?

Answer 17

Gravitational torque (τ) = m × g × r × sin(θ), where m is mass, g is acceleration due to gravity, and r is the distance from the pivot.

Question 18

What is the equation for rotational kinetic energy?

Answer 18

Rotational kinetic energy (KE_rot) = 1/2 Iω².

Question 19

What does a higher moment of inertia imply?

Answer 19

A higher moment of inertia implies that more torque is required to achieve the same angular acceleration.

Question 20

What is the formula for the net torque acting on an object?

Answer 20

Net torque (τ_net) = Στ, the sum of all torques acting on the object.

Question 21

True or False: The direction of torque is determined by the right-hand rule.

Answer 21

True; the right-hand rule helps determine the direction of torque.

Question 22

What is the relationship between torque and rotational motion?

Answer 22

Torque causes rotational motion, analogous to how force causes linear motion.

Question 23

What is the formula for angular acceleration?

Answer 23

Angular acceleration (α) = τ / I, where τ is the net torque and I is the moment of inertia.

Question 24

What is the unit of angular acceleration?

Answer 24

Angular acceleration is measured in radians per second squared (rad/s²).

Question 25

What happens to angular momentum if no external torque acts on a system?

Answer 25

Angular momentum remains constant.

Question 26

What is the relationship between linear and angular displacement?

Answer 26

Linear displacement (s) = r × Δθ, where r is the radius and Δθ is the angular displacement.

Question 27

How does the distribution of mass affect moment of inertia?

Answer 27

The further the mass is distributed from the axis of rotation, the greater the moment of inertia.

Question 28

What is a torque wrench used for?

Answer 28

A torque wrench is used to apply a specific torque to a fastener such as a nut or bolt.

Question 29

What is the formula for the net torque when multiple forces are acting?

Answer 29

Net torque (τ_net) = τ₁ + τ₂ + τ₃ + ..., the sum of all individual torques.

Question 30

What does the term 'lever arm' refer to?

Answer 30

The lever arm is the perpendicular distance from the line of action of the force to the pivot point.

Question 31

What type of motion results from a net torque acting on an object?

Answer 31

A net torque results in angular acceleration and rotational motion.

Question 32

True or False: The moment of inertia for a solid cylinder about its central axis is I = 1/2 m r².

Answer 32

True.

Question 33

What is the moment of inertia for a thin spherical shell about its diameter?

Answer 33

Moment of inertia (I) = 2/3 m r², where m is the mass and r is the radius.

Question 34

What is the effect of increasing the radius of a rotating object on its moment of inertia?

Answer 34

Increasing the radius increases the moment of inertia, making it harder to change its rotational motion.

Question 35

What is the angular displacement for one complete revolution?

Answer 35

The angular displacement for one complete revolution is 2π radians.

Question 36

What is the formula for tangential acceleration?

Answer 36

Tangential acceleration (a_t) = r × α, where r is the radius and α is the angular acceleration.

Question 37

What happens to the angular velocity of a rotating body if its moment of inertia increases but torque remains constant?

Answer 37

The angular velocity will decrease, as ω = τ / I.

Question 38

What is the formula for the gravitational potential energy of an object at height h?

Answer 38

Gravitational potential energy (U) = mgh, where m is mass, g is acceleration due to gravity, and h is height.

Question 39

What is the condition for an object to be in rotational equilibrium?

Answer 39

The net torque acting on the object must be zero.

Question 40

What is the formula for the power in rotational motion?

Answer 40

Power (P) = τ × ω, where τ is torque and ω is angular velocity.

Question 41

What is the unit of power in rotational dynamics?

Answer 41

Power is measured in Watts (W).

Question 42

What is a gyroscope?

Answer 42

A gyroscope is a device that uses angular momentum to maintain orientation.

Question 43

What is rotational inertia?

Answer 43

Rotational inertia is another term for moment of inertia.

Question 44

What is the effect of a torque applied at an angle less than 90 degrees?

Answer 44

The effective torque is reduced, calculated as τ = r × F × sin(θ).