1. Find the area of a sector having a central angle of 60° in a circle of radius 8 inches.

2. Find the perimeter and area of a circular sector whose angle is 3.5 radians if the circumference of the circle is 58 ft.

3. A point on the wheel of radius 10 feet moves with a linear velocity of 40 feet per second. Find the angular velocity of the wheel in radians per second and in RPM

4. Find the speed in radians and in degrees per second of disc revolving at 90 RPM.

5. A belt moving at 60 feet per second drives a pulley at 240 RPM. Find the diameter of the pulley

6. A car's wheel is 3 feet in diameter. Find its angular velocity if the car travels at 60 miles per hour.

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Hello

Please find the solution in the attached file.

1. Find the area of a sector having a central angle of 60° in a circle of radius 8 inches.

2. Find the perimeter and area of a circular sector whose angle is 3.5 radians if the circumference of the circle is 58 ft.

3. A point on the wheel of radius 10 feet moves with a linear ...

Solution Summary

This provides several examples of radian problems, including perimeter and area of sectors, diameter, and velocity.

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 = angularvelocity (or angular frequency) in radians/time or revolutions/time
v = rω, where v

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s.
a) Before slowing, what is the speed of a child on the rim? (in m/s)
b) How many revolutions does the merry-go-round make as it stops?

See attachment please.
Need FBD for each case.
The 0.2 kg ball ( ball is sliding not rotating) and the supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angularvelocity of W = 4 radians/sec. The green ball is held in position b = .3 m by the tension T in the yellow cord.
If b

A pitcher throws a curveball that reaches the catcher in 0.53 s. The ball curves because it is spinning at an average angularvelocity of 335 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?

A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s/s. Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s?

A ceiling fan has one red blade. Initially rotating in a counterclockwise (positive direction) with angularvelocity Wo= +30 radians per second.
SEE THE ATTACHMENT FOR A PICTURE WITH KNOWN DATA.
At that instant, when the red blade makes an angle Qo= +1.4 radians from the +x axis, the current is reversed and a timer is started

Could you please provide the answers and workings out to the following physics problems.
1. A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over 3.0-s interval. What is the angular acceleration of a point on the wheel?
2. During the spin-dry cycle of a washing machine, the motor slo

1. The vector expression of an acceleration can be obtained by:
a. Differentiation position vector once
b. Differentiation velocity vector once
c. Differentiation position vector three times
d. Differentiation velocity vector twice
2. The work of forces acting on a rigid body can be expressed as:
a. the dot product

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?