Name: _______________________________________ Date: _______________________ HR: ______
Trigonometry: 2.3 Linear and Angular Velocity Worksheet
Find the linear velocity of a point moving with uniform circular motion, if the point covers a distance s in
an amount of time t, where (round answers to 3 significant digits)
1.)
s = 3ft and t = 2 min
2.)
s =10 ft and t = 2 min
3.)
s = 12 cm and t = 4 sec
4.)
s = 30 mi and t = 2 hr
Find the distance s covered by a point moving with linear velocity v for a time t if
5.)
v = 20 ft/sec and t = 4 sec
6.)
v = 10 ft/sec and t = 4 sec
7.)
v = 45 mi/hr and t = ½ hr
8.)
v = 21 mi/hr and t = 20 min
Point P sweeps out central angle 𝜃 as it rotates on a circle of radius r as given below. In each case, find
the angular velocity of point P.
2𝜋
9.)
𝜃=
10.)
𝜃=
11.)
𝜃 = 12, 𝑡 = 3 𝑚𝑖𝑛
12.)
𝜃 = 45𝜋 , 𝑡 = 1.2 ℎ𝑟
3
3𝜋
4
, 𝑡 = 5 𝑠𝑒𝑐
, 𝑡 = 5 𝑠𝑒𝑐
In the problems that follow, point P moves with angular velocity 𝜔 on a circle of radius r. In each case,
find the distance s traveled by the point in time t.
𝑟𝑎𝑑
13.)
𝜔 = 4 𝑠𝑒𝑐 , 𝑟 = 2 𝑖𝑛𝑐ℎ𝑒𝑠, 𝑡 = 5 𝑠𝑒𝑐
14.)
𝜔 = 2 𝑠𝑒𝑐 , 𝑟 = 4 𝑖𝑛𝑐ℎ𝑒𝑠, 𝑡 = 5 𝑠𝑒𝑐
15.)
𝜔=
𝑟𝑎𝑑
3𝜋 𝑟𝑎𝑑
2 𝑠𝑒𝑐
, 𝑟 = 4 𝑚, 𝑡 = 30 𝑠𝑒𝑐
For each of the following problems, find the angular velocity, in radians per minute, associated with the
given rpm.
16.)
10 rpm
17.)
33 1/3 rpm
18.)
5.8 rpm
For each of the following problems a point is rotating with uniform circular motion on a circle of radius r.
19.)
Find v if r = 2 inches and 𝜔 = 5 rad/sec.
20.)
Find v if r = 8 inches and 𝜔 = 4 rad/sec.
21.)
Find 𝜔 if r = 6 cm and v = 3 cm/sec.
22.)
Find 𝜔 if r = 3 cm and v = 8 cm/sec.