Circular Motion

Question 1

What kind of force is required to keep an object moving in a circle at constant speed?

Answer 1

A constant centripetal force ( A force applied always towards the center of that circle).

Question 2

An object moving in a circle at a constant speed is accelerating. True or False?

Answer 2

True.
The direction is always changing hence the velocity always changing, where acceleration is defined as the change in velocity over time.

Question 3

What equations(s) can you use to calculate the magnitude of angular speed?

Answer 3

Angular Speed = v/r or Angular speed = 2 x pi x f
Angular speed = s^-1
v = ms^ -1
r = m
f = Hz

Question 4

What is angular acceleration in terms of angular velocity?

Answer 4

a = (Angular velocity)^2 x r
Angular velocity = s^-1
a = ms^-2
r = m

Question 5

What is angular acceleration in terms of velocity?

Answer 5

a = v^2 / r
a = ms^-2
v = ms^-1
r = m

Question 6

What are the equations for centripetal force?

Answer 6

F = mv^2 / r or F = m (angular speed)^2 r
Angular speed = s^-1
v = ms^-1
r = m
F = N
m = kg

Question 7

What is a radian?

Answer 7

The angle of a circle sector such that the radius is equal to the arc length.
Radians are usually written in terms of Pi
i.e. 2 pi = 360 degrees

Question 8

What are the conditions for SHM?

Answer 8

1. Acceleration must be proportional to its displacement from the equilibrium point.
2. It must act towards the equilibrium point.
3. [a] is proportional to [-x]

Question 9

What is the constant proportionally linking acceleration and x?

Answer 9

-(angular speed) ^2 or -k/m

Question 10

What is x as a trig function of t and angular speed?

Answer 10

x = A cos ((angular speed)t) or x = sin ((angular speed)t)
A = amplitude
x = displacement
t = time

Question 11

How can one calculate the maximum speed using angular speed and Amplitude?

Answer 11

max speed = (angular speed)A

Question 12

How can one calculate the maximum acceleration using angular velocity and A?

Answer 12

Max acceleration = (angular speed)A

Question 13

What is the equation for the time period of a mass- spring simple harmonic system?

Answer 13

T = 2 pi sq.rt: (m/k)
m - kg
k - Nm-1
T - s

Question 14

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

Answer 14

T = 2 pi sq.rt: (L/g)
g - ms^-2
L - m
T - s

Question 15

What is the small angle approximation for sin x?

Answer 15

sin x is approximately x
valid in radians

Question 16

What is the small angle approximation for cos x?

Answer 16

cos x is approximately 1- x^2 / 2
valid in radians

Question 17

Draw the graph for potential energy and kinetic energy against displacement, for a SHM system?

Answer 17

https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/15-2-energy-in-simple-harmonic-motion/

Question 18

Define Free vibrations.

Answer 18

The frequency a system tends to vibrate at in a free vibration is called the natural frequency

Question 19

Define Forced vibrations.

Answer 19

1. A driving force that causes the system to vibrate at different frequency.
2. For higher driving frequencies, the phase difference between the driver and the oscillations rises to pi radians.
3. For lower frequencies, the oscillations are in phase with the driving force
4. When resonance occurs, which is when it most efficiently transfers energy to the system, The phase difference will be pi/2 radians

Question 20

Define damping and explain what is critical damping, overdamping and underdamping.

Answer 20

1. Damping occurs when an opposing force dissipates energy to the surroundings
2. Critical damping reduces the amplitude to zero in the quickest time.
3. Overdamping is when the damping force is too strong and it returns to equilibrium slowly without oscillation
4. Underdamping is when the damping force is too weak and it oscillates with exponentially decreasing amplitude

Question 21

What happens to a vibration with greater damping?

Answer 21

1. For a vibration with greater damping, the amplitude is lower at all frequencies due to greater energy losses from the system.
2. The resonant peak is also broader because of the damping

Question 22

What are some applications of resonance in real life?

Answer 22

Implications of resonance include that soldiers must break stop when crossing bridges and vehicles must be designed so there are no unwanted vibrations.