12.2.2Circular motion and gravitational fields (A Level)
Calculating Centripetal Acceleration
5 min read 7 parts Lesson 4 of 14 1 quiz
Lesson summary
12.2.2 Calculating Centripetal Acceleration — AS PHYSICS 9702 notes: Use a = v²/r and a = rω² to calculate centripetal acceleration.Centripetal acceleration — the acceleration of an object towards the centre of a circle when it moves around the circle at constant speed.Direction …
- What the symbols mean
- Doubling the radius and angular speed
- Linear speed
- Direction — towards the centre, perpendicular to the object’s velocity
- r is radius in m
- Use the link v = rω, with ω in rad s−1
Section 1 of 7Definition
Centripetal acceleration
- Centripetal acceleration the acceleration of an object towards the centre of a circle when it moves around the circle at constant speed.
Direction
- Direction towards the centre, perpendicular to the object’s velocity.
Section 2 of 7In terms of linear speed
- Equation
- a = v2/r.What the symbols mean: a = centripetal acceleration towards the centre (m s−2) · v = speed (m s−1) · ω = angular speed (rad s−1) · r = radius (m)
- a is centripetal acceleration in m s−2.
- v is linear speed in m s−1.
- r is radius in m.
- a = v2/r.
Section 3 of 7In terms of angular speed
In terms of angular speed
Use the link v = rω, with ω in rad s−1.
Substitute into a = v2/r to get a = (rω)2/r.
Simplify to a = rω2.
Section 4 of 7Effect of changing quantities
Effect of changing quantities
Doubling the radius and angular speed
- Doubling the radius and angular speed a = rω2 becomes 2r × (2ω)2 = 8rω2, eight times bigger.
Method
- Method state the equation, apply the changes, then substitute values.
Units
- Units keep angular speed in rad s−1.
Section 5 of 7More from the specification
More from the specification
Centripetal requirement and real forces
- Centripetal requirement and real forces tension, gravitational attraction,
- or friction act as physical forces supplying the necessary inward centripetal acceleration.
Centripetal Acceleration in Uniform Circular Motion
- An object travelling along a circular path at constant speed undergoes uniform circular motion;
- its direction constantly changes,
- which causes a continuous inward centripetal acceleration defined by a = v²/r = ω²r.
Centripetal Force Magnitude
- By Newton's second law, centripetal acceleration requires a resultant inward centripetal force of magnitude F = m·v²/r = m·ω²r, measured in newtons (N).
Vertical Circular Motion Example
- For a bucket of water whirled in a vertical circle, the minimum speed at the top to prevent spilling occurs when the required centripetal force is provided solely by the bucket's downward weight (vmin = √(g·r)).
Circular motion
- Motion along a circular path with a force towards the centre.
Uniform
- Same density throughout, so the weight acts at the centre.
Force
- A push or pull measured in newtons.
Vector
- Quantity with magnitude and direction.
Tangent
- Line touching a curve; its slope gives the instantaneous rate.
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Centripetal acceleration | Acceleration of an object towards the centre of its circular path. |
| Angular speed | Rate of change of angular displacement, in rad s⁻¹. |
| Linear speed | Speed along the circular path, v = rω. |
| Radius | Distance from the centre to the circular path. |
Section 7 of 7Exam technique
1
Using ω in degrees per second instead of rad s⁻¹.
2
Forgetting to square v or ω.
3
Using the diameter in place of the radius.
4
Thinking the acceleration points along the velocity.