Topic: Circular Motion
Class: SS1
Specific Objectives:
By the end of this lesson, students should be able to:
- Define circular motion.
- Explain centripetal force and acceleration.
- Solve problems involving circular motion.
Instructional Materials:
- String
- Small object (stone or ball)
- Stopwatch
- Chalkboard/Whiteboard
Step 1: Circular Motion
Circular motion occurs when an object moves along a circular path. The object constantly changes direction while moving at a certain speed along the path.
- Example: A stone tied to a string spun in a circle.
- The object always moves tangentially to the circle, while a force keeps it moving along the curve.
Activity: Students tie a small object to a string and spin it. Observe the motion and note the direction of the string’s pull.
Step 2: Centripetal Force
Centripetal force is the force that keeps an object moving along a circular path. It always points toward the center of the circle.
Fc = (m * v²) / r
Where:
-
Fc = centripetal force (N)
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m = mass of object (kg)
-
v = speed of object (m/s)
-
r = radius of the circular path (m)
-
Example: A 2 kg object moves at 4 m/s in a circle of radius 2 m.
Fc = (2 * 4²) / 2 = (2 * 16) / 2 = 32 / 2 = 16 N
Activity: Students calculate the centripetal force for a toy car moving in a circular path on a smooth surface.
Step 3: Centripetal Acceleration
Centripetal acceleration is the acceleration directed toward the center of the circle that keeps an object moving along the circular path.
ac = v² / r
- Example: A stone moves in a circle of radius 0.5 m at 3 m/s.
ac = 3² ÷ 0.5 = 9 ÷ 0.5 = 18 m/s²
- Centripetal acceleration is always perpendicular to the object’s instantaneous velocity.
Activity: Students measure speed and radius of circular motion of a toy car or spinning object, then calculate centripetal acceleration.
Step 4: Relation Between Force and Acceleration in Circular Motion
- Centripetal force = mass × centripetal acceleration:
Fc = m * ac
- Example: A 1.5 kg object moves at 6 m/s in a circle of radius 3 m.
ac = v² / r = 6² / 3 = 36 / 3 = 12 m/s²
Fc = m * ac = 1.5 * 12 = 18 N
Activity: Students are given different radii and velocities, and they calculate the required centripetal force.
Step 5: Everyday Examples of Circular Motion
- A car turning a circular curve on the road.
- A satellite orbiting the Earth.
- A ceiling fan blade moving in a circle.
Activity: Students list other examples of circular motion and identify the centripetal forces involved.
Summary
- Circular motion is motion along a curved path.
- Centripetal force keeps the object moving in a circle, always toward the center.
- Centripetal acceleration is the acceleration toward the center, calculated as v²/r.
- Fc = m * ac relates mass, acceleration, and force.
Evaluation
- Define circular motion.
- Calculate centripetal force for a 2 kg object moving at 5 m/s in a circle of radius 2 m.
- Determine centripetal acceleration of a 3 kg object moving at 4 m/s in a circle of radius 0.5 m.
Class Work
- A stone of mass 0.5 kg moves in a circle of radius 1 m at 2 m/s. Calculate centripetal acceleration.
- Find the centripetal force on a 3 kg toy car moving at 6 m/s in a circle of radius 2 m.
- List three real-life examples of circular motion and identify the centripetal force in each.
Home Work
- Explain why centripetal force is always directed toward the center of a circle.
- A car of mass 1,000 kg rounds a curve of radius 50 m at 20 m/s. Calculate the centripetal force.
- Determine the centripetal acceleration for a satellite orbiting Earth at a speed of 8,000 m/s and a radius of 6,700 km.
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