Question:
Answer:
Uniform Circular Motion
The following are the formulas and symbols for use in the following calculations.
Period (T) = 1/f
Frequency (f)=1/T
V= (rw) rate of change of displacement with time
r- Radius as and omega (w) the rate of change of angle with respect to time
Start velocity (u) and end velocity (v)
- f=1/T
= 1/5
=0.2Hz
- a).Distance(radius) =19mm
Total distance for the needle moves= 2πr
=2π19
=119.380mm
b).The average velocity =Total displacement/Total time
=119.380/1 (since frequency and period is constant)
=119.380mm/seconds
- a).The needle point needs maximum velocity when the acceleration for the shaft is zero and that is achieved when the at the angle of 0,45,180 and at 270 degrees respectively.
b).At maximum acceleration, the velocity of the point needle needs to be at zero at for this case it will be at 0 and 180 degrees respectively.
- a. v= rw
=19/1000*3
=0.057 Rad/second
- b) Tangential velocity= 119.380/12seconds
=9.95m/s
- If time at the top of the needle shaft has a motion at zero 0, the time it will have moved 22mm from the top can be arrived to as follows:
Let the start velocity =0 at zero displacement. We assume that velocity at 22mm would be 0.
Time= Displacement/Velocity
=22mm/0,
This gives an indefinite figure.
- Time for a velocity of 3mm/s would be
Time =Displacement /Velocity
=22mm/3mm/s
= 7.33seconds.
- Time the needle shaft first experiences acceleration of 4mm/s/s
Acceleration (a)=(v-u)/t
4=3/t since the velocity is quoted for above to be 3m/s
Time= 3*4mm/s
= 12 seconds
- Position of the needle shaft at first time acceleration is at 3mm/s/s Displacement = Acceleration * time (acceleration is same as velocity for this case since it picks off at u=0 and attains v=3)
= 3* 7.33
=22 mm.
References
Fuente, D., Romero, A., & Torres, P. J. (2017). Uniform circular motion in general relativity: existence and extendibility of the trajectories. Classical and Quantum Gravity, 34(12).
Sunarno, W. (2017, January). Uniform circular motion concept attainment through circle share learning model using real media. In Journal of Physics: Conference Series (Vol. 795, No. 1, p. 012053). IOP Publishing.
