the angular speed of abody which executes uniform circular motion with period 2sis
Answers
We know that
T = 2π/ω
ω=2π/T
ω= π
angular speed is π
Hope this helps
Answer:
Explanation:
Term (symbol) Meaning
Uniform circular motion Motion in a circle at a constant speed
Radian Ratio of an arc’s length to its radius. There are 2\pi2π2, pi radians in a 360 \degree360°360, degree circle or one revolution. Unitless.
Angular velocity (\omegaωomega) Measure of how an angle changes over time. The rotational analogue of linear velocity. Vector quantity with counterclockwise defined as the positive direction. SI units of \dfrac{\text{radians}}{\text {s}}
s
radians
start fraction, start text, r, a, d, i, a, n, s, end text, divided by, start text, s, end text, end fraction.
Centripetal acceleration (a_ca
c
a, start subscript, c, end subscript) Acceleration pointed towards the center of a curved path and perpendicular to the object’s velocity. Causes an object to change its direction and not its speed along a circular pathway. Also called radial acceleration. SI units are \dfrac{\text m}{\text s^2}
s
2
m
start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction.
Period (TTT) Time needed for one revolution. Inversely proportional to frequency. SI units of \text{s}sstart text, s, end text.
Frequency (fff) Number of revolutions per second for a rotating object. SI units of \dfrac{1}{\text{s}}
s
1
start fraction, 1, divided by, start text, s, end text, end fraction or \text{Hertz (Hz)}Hertz (Hz)start text, H, e, r, t, z, space, left parenthesis, H, z, right parenthesis, end text.
Equations
Equation Symbol breakdown Meaning in words
\Delta \theta = \dfrac{\Delta s}{r}Δθ=
r
Δs
delta, theta, equals, start fraction, delta, s, divided by, r, end fraction \Delta \thetaΔθdelta, theta is the rotation angle, \Delta sΔsdelta, s is the distance traveled around a circle, and rrr is radius The change in angle (in radians) is the ratio of distance travelled around the circle to the circle’s radius.
\bar \omega = \dfrac{\Delta\theta}{\Delta t}
ω
ˉ
=
Δt
Δθ
omega, with, \bar, on top, equals, start fraction, delta, theta, divided by, delta, t, end fraction \bar \omega
ω
ˉ
omega, with, \bar, on top is the average angular velocity, \Delta\thetaΔθdelta, theta is rotation angle, and \Delta tΔtdelta, t is change in time Average angular velocity is proportional to angular displacement and inversely proportional to time.
v = r \omegav=rωv, equals, r, omega vvv is linear speed, rrr is radius, \omegaωomega is angular speed. Linear speed is proportional to angular speed times radius rrr. Angular speed is the magnitude of the angular velocity.
T = \dfrac{2\pi}{\omega} = \dfrac{1}{f}T=
ω
2π
=
f
1
T, equals, start fraction, 2, pi, divided by, omega, end fraction, equals, start fraction, 1, divided by, f, end fraction TTT is period, \omegaωomega is angular speed, and fff is frequency Period is inversely proportional to angular speed times a factor of 2\pi2π2, pi, and inversely proportional to frequency.
How to relate angular speed and linear speed
Angular velocity \omegaωomega measures the amount of rotation per time. It is a vector and has a direction which corresponds to counterclockwise or clockwise motion (Figure 1). [How can counterclockwise be a direction?]