Physics Problems - Angle conversions and using Radians

1. Convert the following angles from degrees to radians, to three significant figures: a) 15°, b) 45°, c) 90° and d) 120°.

2. A jogger on a circular track that has a radius of 0.250km runs a distance of 1.00 km. What angular distance does the jogger cover in a) radians and b) degrees?

3. In Europe, a large circular walking track with a diameter of 0.900 km is marked in angular distances in radians. An American tourist who walks 3.00 mi daily goes to the track. How many radians should he walk per day to maintain his daily routine?

4. Electrical wire with a diameter of 0.50cm is would on a spool with a radius of 30 cm and a height of 24cm. a) Through how many radians must the spool be turned to wrap one even layer of wire? B) What is the length of this wound wire?

5. If a particle is rotating with an angular speed of 3.5 rad/s, how does it take for the particle to go through one revolution?

Solution Summary

The solution goes over a number of physics problems relating to the use of angles, degrees, and radians.

A 12-in. diameter phonograph record rotates about its center by one-quarter turn.
a. Through how many radians has it turned?
b. How far has a point on the rim moved?

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s squared. Through what angle does the pulley turn in 5.26 s?

In this question ABC and PQR are two triangles, and the lengths of the sides opposite the angles A,B,C P, Q, R are a,b,c,p,q,r, respectively.
Choose the THREE false statements.
Options.
A. If angle A= angle Q andangle B= angle P. then it must follow that c b
--- = --
r p
B. I

1.) The engine of a sports car rotates at 5,000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2 radians = 1 revolution.
2.) Convert -60° to radians. Express the answer as a multiple of π
3.) Draw the following angle in standard the position:
4.) In which q

I am having problems interpreting what sin(x/4) is . I have done a graph for sin(X) and sin(x/4) from 0 to 12pi on the x axis,and this makes the x axis go to about 37.699111 radians. The sin(x) goes from 0 up to +1 on the y axis, this is about 90 degrees. Then it goes back through the x axis at about 3, then down to y-1, this is

A projectile being fired upward at an angle to the horizontal, θ. You are to program the spreadsheet Excel (a similar substitute software program is permissible) to determine the maximum injection angle, θmax , that will result in the greatest downrange distance, R. Assume vo = 10 m/s and g is approximated as g = 10

2π radians = 360 degrees = 1 cycle = 1 revolution
T (period in time/cycle) = 1/f (frequency in cycles/time), and ω = 2πf
For circular motion: s = rθ, where s = distance in units of length, r = radius, θ = angle in radians
ω = angular velocity (or angular frequency) in radians/time or revolutions/time
v = rω, where v

Please give detailed explanation.
Please see attached file for full problem description.
Solve, finding all solutions in [0, 2) and [0, 360). Express solutions in both radiansand degrees.
tan = 1 / 3

Please see the attached file for all of the fully formatted problems.
1. You have calibrated your voltmeter so that you know a meter reading
of 10 V is actually 10.2 V and a reading of 15 V is actually 15.6 V.
What is the actual voltage when your meter reads 12.3 V?
(1) 11.9V (3) 12.3 V (5) 13.1 V
(2) 12.1 V (4) 12.7 V (6