# 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?

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#### Solution Summary

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

Mechanics Problems

How many significant numbers do each of the following numbers have?

a. 214

b. 81.60

c. 7.03

d. 0.03

e. 0.0086

f. 3236

g. 8700

NOTE the 10 with a number after in () is power of ten/ scientific Notation

Write the following numbers in full with the correct number of zeros.

a. 8.69x10(4)

b. 9.1x10(3)

c. 8.8x10(-1)

d. 4.76x10(2)

e. 3.62x10(-5)

Add (9.2x10(3)s) +8.3x10(4)s)+(0.0008x10(6)s)

What is the conversion factor between.

a. ft(2) and yd(2)

b. m(2) and ft(2)

A bird can fly 25km/h. How long does it take to fly 15km?

A particle at t1= -2.0s is at x1=3.4cm and at t2 = 4.5s is at x2 = 8.5cm What is the average velocity? Calculate its average speed from these data?

Calculate the average speed and average velocity of a complete round trip in which the out going 250km is covered at 95km/h, followed by a 1.0 hour lunch break, and return 250km is covered at 55km/h?

If a car rolls gently v0=0 off a vertical cliff how long does it take to reach 85km/h

A delivery truck travels 18 blocks north, 10 blocks east and 16 blocks south, What is the final displacement from the orgin? Assume the block are equal.

A diver running 1.8m/s dives out horizontally from the edge of a vertical cliff and 3.0s later reaches the water below. How high was the cliff, and how far from its base did the diver hit the water?

An athlete executing a long jump leaves the ground at a 28.0 degree angle and travels 7.80m.

a. What was the take off speed?

b. If the speed was increased by just 5.0% how much longer would the jump be?

Show that the speed with which a projectile leaves the ground is equal ti its speed just before it strikes the ground at the end of its journey, assuming the firing level equals the landing level.

What is the weight of a 76kg astronaut.

a. on earth

b. on the moon(g=1.7m/s(2))

c. on Mars(g=3.7m/s(2))

d. in outer space traveling with constant velocity

Suppose that you are standing on a train accelerating at 0.02g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?

A car can decelerate at -4.80m/s(2) without skidding when coming to rest on a level road. What would its deceleration be if the incline were at 13 degrees uphill?

Assume the same static friction coefficient.

The idea that that one law can cause another is called:

(a) probability

(b) causality

(c) kepler

(d) event

The product of the magnitude of the displacement times the component of the force parallel to the displacement is called:

(a) energy

(b) work

(c) joule

(d) force

Observations of the motion of bodies indicate that even if a body rotates, or there are several bodies that move relative to one another, there is a point that moves in the same in the same path that a particle would be subjected to the same net force. This point is called:

(a) gravitational center

(b) center of gravity

(c) center of matter

(d) center of mass

The angular acceleration, then, is proportional to the product of the force times the lever arm. This product is called the momentum of the force about the axis or more commonly called:

(a) radian

(b) force

(c) torque

(d) energy