Advertisements
Advertisements
Question
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
Options
π
2 π
4 π
8 π
Advertisements
Solution
8 π
\[\text{ Angular velocity }= \frac{\text{Distance}}{\text{Time}}\]
\[ = \frac{4 \text{ revolutions}}{1\text{ second}}\]
\[ = \frac{4 \times 2\pi}{1} \left( \because 1\text{ revolution }= 2\pi \text{ radians }\right)\]
\[ = 8\pi \text{ radians per second }\]
APPEARS IN
RELATED QUESTIONS
Find the radian measure corresponding to the following degree measure:
240°
Find the radian measure corresponding to the following degree measure:
520°
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm
(Use `pi = 22/7`)
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]
Find the degree measure corresponding to the following radian measure:
11c
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 7° 30'
The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.
The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.
The angle between the minute and hour hands of a clock at 8:30 is
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
The value of tan1° tan2° tan3° ... tan89° is ______.
The value of cos1° cos2° cos3° ... cos179° is ______.
State whether the statement is True or False? Also give justification.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
State whether the statement is True or False? Also give justification.
Sin10° is greater than cos10°
State whether the statement is True or False? Also give justification.
`cos (2pi)/15 cos (4pi)/15 cos (8pi)/15 cos (16pi)/15 = 1/16`
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
