Further Mechanics

Question 1

What is the condition for an object moving in a circle?

Answer 1

There must be a force that continuously acts at 90 degrees to the object’s velocity.

Question 2

How does velocity change for an object moving in a circle?

Answer 2

Its velocity and direction of travel constantly change, but it still travels at a constant speed.

Question 3

Why is an object moving in a circle considered to be accelerating?

Answer 3

Because the direction of the velocity is changing, even though the magnitude of the velocity (the speed) is not.

Question 4

What is the formula for centripetal acceleration?

Answer 4

Centripetal acceleration is equal to v squared over r, where r is the radius of the circle.

Question 5

What is the formula for centripetal force?

Answer 5

Centripetal force is equal to mv squared over r.

Question 6

How can speed be calculated in circular motion?

Answer 6

Speed can be calculated by doing circumference divided by the time period, so 2 pi r over t.

Question 7

What is angular velocity?

Answer 7

Angular velocity, symbolized by omega (ω), is how many radians of the orbit are covered every second.

Question 8

What is the relationship between linear velocity and angular velocity?

Answer 8

v equals omega r.

Question 9

What does normal frequency equal?

Answer 9

Normal frequency equals 1 over the time period.

Question 10

What alternative equations can be derived for centripetal acceleration and force?

Answer 10

a equals omega squared r and f equals m omega squared r.

Question 11

How do you use the omega version of the equations?

Answer 11

If given the time period, replace omega with 2 pi over t.

Question 12

When should you use the v squared over r equation?

Answer 12

Use a equals v squared over r or f equals mv squared over r when given the actual speed.

Question 13

How is angular displacement defined?

Answer 13

Angular displacement is how many radians an object has turned through.

Question 14

How do you convert degrees to radians?

Answer 14

To convert degrees to radians, divide by 360 to turn into whole circles, then multiply by 2 pi.

Question 15

What forces are considered in a vertical loop, like on a roller coaster?

Answer 15

At the bottom, mg is pulling down and the support force (s) is pushing up.

Question 16

How is centripetal force calculated at the top of a vertical loop?

Answer 16

Centripetal force equals s plus mg.

Question 17

What happens to weight when an object is at the sides of a vertical loop?

Answer 17

Weight isn’t contributing to the centripetal force, therefore s equals mv squared over r.

Question 18

What is the main force on a car on a banked track?

Answer 18

The main force is the perpendicular reaction force of the track, which is at an angle.

Question 19

What is the centripetal force in circular motion?

Answer 19

The centripetal force is equal to the weight mg and points towards the center of the circular path.

Question 20

How is the horizontal force related to weight and angle?

Answer 20

The horizontal force is equal to mg tan theta, where mg is the weight.

Question 21

What describes simple harmonic motion (SHM)?

Answer 21

SHM describes any object oscillating around a point, such as a pendulum or mass on a spring.

Question 22

What are the two conditions for acceleration in SHM?

Answer 22

1. Acceleration must be proportional to the object’s displacement from equilibrium. 2. It must be in the opposite direction to the displacement.

Question 23

What is the restoring force in SHM?

Answer 23

The restoring force is the force trying to return the object to equilibrium.

Question 24

What does the equation a = -ω²x represent?

Answer 24

It shows the relationship between acceleration, displacement, and angular frequency in SHM.

Question 25

What is the maximum acceleration in SHM?

Answer 25

The maximum acceleration occurs at the maximum displacement, known as the amplitude (A). ## Footnote a_max = ω²A.

Question 26

What type of graph represents displacement over time in SHM?

Answer 26

The graph of displacement changes with time for SHM is a sine graph if it starts at zero, or a cosine graph if it starts at amplitude.

Question 27

How do you find the maximum velocity in SHM?

Answer 27

The maximum velocity (v_max) is given by v_max = ωA or v_max = 2πfA.

Question 28

What is the relationship between kinetic energy and total energy in SHM?

Answer 28

The maximum kinetic energy is equal to the total energy of the system.

Question 29

What is the equation for the time period of a pendulum?

Answer 29

The time period (T) of a pendulum is T = 2π√(l/g), where l is the length of the string and g is gravitational field strength.

Question 30

What is the time period equation for a mass on a spring?

Answer 30

The time period (T) for a mass on a spring is T = 2π√(m/k), where k is the spring constant.

Question 31

What happens to the frequency of a pendulum if the length is doubled?

Answer 31

The time period increases by a factor of √2, which means the frequency decreases.

Question 32

What is light damping?

Answer 32

Light damping is when the amplitude of oscillations decreases gradually over time.

Question 33

What is heavy damping?

Answer 33

Heavy damping occurs when the resistive force is large enough that the object does not oscillate, and its displacement gradually decreases.

Question 34

What is critical damping?

Answer 34

Critical damping is when damping forces ensure the object comes to a stop at equilibrium as quickly as possible.

Question 35

What is resonance?

Answer 35

Resonance occurs when an external force drives the oscillations, increasing the amplitude and adding energy to the system.

Question 36

What is the condition for maximum resonance?

Answer 36

Maximum resonance occurs when the frequency of the driving force matches the natural frequency of the system.

Question 37

What happens to the resonance peak with increased damping?

Answer 37

The height of the resonance peak decreases as damping increases, but the peak does not get narrower.