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India
Class XI

Use Linear and Angular Speed Formulas

Interactive practice questions

Consider the following diagram, in which point $P$P is rotating anticlockwise around the unit circle at a constant velocity.

a

Fill in the blank: The measure of how fast the position of point $P$P is changing is the ___________.

Angular speed (or velocity)

A

Linear speed (or velocity)

B

Quadratic speed (or velocity)

C

Circular speed (or velocity)

D
b

Fill in the blank: The measure of how fast the angle $\theta$θ is changing is the ______.

Angular speed (or velocity)

A

Circular speed (or velocity)

B

Linear speed (or velocity)

C

Spiral speed (or velocity)

D
c

If the angular speed of point $P$P is $\frac{\pi}{4}$π4 radians/sec, what is the linear speed of point $P$P?

d

If $P$P is rotating with an angular speed of $\frac{\pi}{2}$π2 radians/sec, how far will $P$P travel in $20$20 seconds?

Easy
5min

If the angular speed $\omega=\frac{\pi}{5}$ω=π5 radians per second and the rotation time $t=8$t=8 seconds, find the rotation angle $\theta$θ.

Easy
1min

An object moves along the edge of a circular disc at $\omega=\frac{5\pi}{6}$ω=5π6 radians per second. The disc has a radius $r=9$r=9 yards.

Find the distance $s$s along the edge of the disc that the object will travel in $t=8$t=8 seconds.

Easy
3min

Tobias is riding a motorbike with wheels that have a diametre of $80$80cm and that are rotating at $42$42 radians per second.

Easy
5min
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Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

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