Advertisements
Advertisements
Question
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
Advertisements
Solution
Number of revolutions taken by the wheel in 1 minute = 360
\[\text{ Number of revolutions taken by the wheel in 1 second }= \frac{360}{60} = 6\]
We know:
\[\text{ 1 revolution }= 2\pi \text{ radians }\]
\[ \therefore \text{ Number of radians the wheel will turn in 1 second }= 6 \times 2\pi = 12\pi \]
APPEARS IN
RELATED QUESTIONS
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the radian measure corresponding to the following degree measure:
240°
Find the degree measure corresponding to the following radian measure `(use pi = 22/7)`
`11/16`
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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`)
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
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:
11c
Find the radian measure corresponding to the following degree measure: 35°
Find the radian measure corresponding to the following degree measure: −56°
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 125° 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 octagon.
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 angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.
Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
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.
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?
Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
The angle between the minute and hour hands of a clock at 8:30 is
At 3:40, the hour and minute hands of a clock are inclined at
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 tan 9° – tan 27° – tan 63° + tan 81°
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
If tan θ = `(-4)/3`, then sin θ is ______.
The value of tan1° tan2° tan3° ... tan89° is ______.
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.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
