Circular Motion: Concepts and Learning Outcomes

Why is it important to define radian as a unit of measuring angle in circular motion?

• It helps in measuring mass

• It is necessary for calculating angular displacement

• It is used to find linear speed

• It is required for energy calculations

Which of the following is NOT a unit for measuring angles?

• Degree (°)

• Radians (rad)

• Revolution (rev)

• Meter (m)

If an angle measures 3π/2 radians, what is its equivalent in degrees?

• 270°

• 180°

• 90°

• 360°

How is a radian used to measure angles?

• By relating the length of an arc to the radius of a circle.

• By measuring the diameter of a circle.

• By counting the number of rotations.

• By dividing a circle into 100 equal parts.

If an angle θ at the center of a circle subtends an arc equal in length to the radius of the circle, what is the measure of θ in radians?

• 2π rad

• 1 rad

• π rad

• 57.3 rad

Which of the following expressions correctly converts 14 radians to degrees?

• 14 × 180/π

• 14 × π/180

• 14 ÷ 180/π

• 14 + 180/π

Which of the following is a reason why radians are often preferred over degrees in mathematical calculations?

• Radians are easier to convert to fractions

• Radians are natural in calculus and make many theorems simpler

• Degrees are more commonly used in daily life

• Degrees simplify trigonometric functions

How many track winds are there on the CD according to the solution?

• 2,608

• 25,000

• 20,625

• 5,400

Given the spiral path in the garden, what is C̅, the average circumference of the loops?

• 50.2 m

• 31.4 m

• 25.1 m

• 40.8 m

What is L, the total length of the spiral path described in the example?

• 188.4 m

• 125.6 m

• 94.2 m

• 150.0 m