Question

A truck with 16-inch radius wheels is driven at 77 feet per second (52.5 miles per hour). Find the

measure of the angle through which a point on the outside of the wheel travels each second. Round to the nearest
degree and nearest radian.

Answer 1

The measure of the angle through which a point on the outside of the wheel travels each second is approximately 57.75 radians per second. When converted to revolutions per minute, it is approximately 548.18 rev/min.

Step-by-step explanation:

To find the measure of the angle through which a point on the outside of the wheel travels each second, we need to calculate the angular velocity.
The formula to calculate angular velocity is ω = v / r, where ω is the angular velocity, v is the linear velocity, and r is the radius of the wheel.
Plugging in the values, we have ω = 77 ft/s / 16 in. Converting the radius to feet, we get ω = 77 ft/s / (16/12) ft = 57.75 rad/s.

Conversion to rev/min

To convert the angular velocity from radians per second to revolutions per minute, we can use the conversion factor 1 revolution = 2π radians.
So, the angular velocity in revolutions per minute is (57.75 rad/s * 60 s/min) / (2π rad/rotation) = 548.18 rev/min.

Answer 2

Given Information:

Radius of wheel = r = 16 inches

Linear speed = v = 77 ft/sec

Required Information:

Angle in radian = ?

Angle in degree = ?

Answer:

Angle in radian = 58 rad/sec

Angle in degree = 3309 deg/sec

Step-by-step explanation:

As we know the relation between linear and angular speed is given by

v = rω

ω = v/r

First convert linear speed from feet/sec to inches/sec

1 foot has 12 inches

77*12 = 924 in/sec

ω = v/r

ω = 924/16

ω = 57.75 rad/sec

ω ≈ 58 rad/sec

Now convert rad/sec to deg/sec

ω = 58*(180°/π)

ω = 3308.8 deg/sec

ω ≈ 3309 deg/sec