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
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:
520°
Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
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
15 cm
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:
(−3)c
Find the degree measure corresponding to the following radian measure:
11c
Find the radian measure corresponding to the following degree measure: 35°
Find the radian measure corresponding to the following degree measure: 7° 30'
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 heptagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
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 number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
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?
Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
At 3:40, the hour and minute hands of a clock are inclined at
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
Find the value of `sqrt(3)` cosec 20° – sec 20°
If θ lies in the second quadrant, then show that `sqrt((1 - sin theta)/(1 + sin theta)) + sqrt((1 + sin theta)/(1 - sin theta))` = −2sec θ
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
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.
`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.
