1. A point on the edge of a large wheel of radius 0.45 meters moves through an angle of 170o at a constant angular velocity of 0.25 radians/sec.

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(a) Find the length (in meters) of the arc described by the point.

(b) Find the linear velocity (in m/sec) of a point located on the edge of the wheel.

(c) Determine the angular acceleration (in radians/sec2) of the wheel.

a. Circumference = pi * 2r = 3.14 * 0.9 = 2.83 m.

Arc = 2.83m/360o * 170o = 1.33 m.

b. V = 0.25rad/s * 2.83m/6.28rads = 0.113 m/s.

c. If the velocity is constant, the acceleration is zero.

To find the length of the arc described by the point, we can use the formula:

Arc length = radius * angle

Given that the radius of the wheel is 0.45 meters and the angle is 170 degrees, we first need to convert the angle to radians:

Angle in radians = Angle in degrees * (pi/180)

Angle in radians = 170 * (pi/180) ≈ 2.967 radians

Now we can calculate the arc length:

Arc length = 0.45 * 2.967 ≈ 1.335 meters

Therefore, the length of the arc described by the point is approximately 1.335 meters.

To find the linear velocity of a point located on the edge of the wheel, we can use the formula:

Linear velocity = radius * angular velocity

Given that the radius is 0.45 meters and the angular velocity is 0.25 radians/sec, we can calculate the linear velocity:

Linear velocity = 0.45 * 0.25 = 0.1125 m/sec

Therefore, the linear velocity of a point located on the edge of the wheel is 0.1125 m/sec.

To determine the angular acceleration of the wheel, we need to know the relationship between angular acceleration, linear acceleration, and radius. However, the question does not provide any information about linear acceleration or radius.

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