Circular Motion

Circular Motion Equations

Centripetal Acceleration, Velocity, and Force

← Uniform Circular Motion All Lessons Relationships →
Do Now warm-up prompt

Do Now

At point P, the car hits an area of ice and loses all frictional force on its tires. Which path does the car follow on the ice?

Regents diagram showing a car on a curved track approaching point P, with several possible path choices

June 2001 Regents

↓

B,

Tangent to the semi-circle

Review - Velocity, Circular Motion

Tangent velocity video thumbnail

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A. Equations & Vectors

Unicycle circling

Review

Given

Why is an object moving at constant speed in a circle considered to be accelerating?

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Because while its speed is not changing, its direction is.

1. Centripetal Acceleration (ac) - acceleration toward center of curvature

Equation:

ac = V² / r

r - radius,
V - velocity

b) (V) Instantaneous Velocity - tangent to circle, in the direction of the motion

c) Centripetal Force (Fc) - force directed toward the center of the circle

Highlander shot put circling

Ex

Given

A car moving in a circular path with a radius of 2.0 m has a velocity of 8.0 m/s.
Find: the centripetal acceleration of this car.

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ac = V² / r
= (8.0 m/s)² / 2.0 m

ac = 64 / 2

ac = 32. m/s²

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Circular Velocity Game (Flash)

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Frisbee
Giancoli p. 130) 2, 4
Top-down view of the spinning Gravitron: the rider's velocity points along the circle while the centripetal acceleration points toward the center, with v = 2 pi r over T and a_c = v squared over r NYSSLS Reading Passage icon

NYSSLS Reading Passage · Dynamics

The Centripetal Dynamic of the Gravitron

Open Reading Passage → Regents Practice Version →

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. Why is an object moving at constant speed in a circle considered to be accelerating?

2. A car moves in a circle of radius 2.0 m at 8.0 m/s. What is its centripetal acceleration?

3. What is the direction of the centripetal acceleration of an object in uniform circular motion?

4. An object moves at 10 m/s in a circle of radius 5.0 m. What is its centripetal acceleration?

5. A car on a curved track hits ice at point P and loses all friction. Which path does it follow?

NYSSLS Regents Practice · Circular Motion · Technology

The Washing Machine Spin Cycle

During a spin cycle, the drum of a washing machine has a radius of 0.25 m. Clothes pressed against the drum wall move in a circle at a constant speed of 8.0 m/s. The drum wall has small holes.

What is the centripetal acceleration of the clothes?

▶ Want a challenge? Open 6 more Regents-style questions  (harder · mixed formats)

Challenge score: 0 / 6

Substitute values

C1. Substitute numerical values into a mathematical representation that can be used to determine the period of the drum’s rotation. Then calculate the period.

T = 2π( m)( m/s) = s
Multiple choice

C2. Why does water leave the clothes through the holes?

Draw the vector · Determine the magnitude

C3. Looking at the front of the machine, the drum turns in a vertical circle. A 0.50-kg wet sock is at the very top of the drum. Choose the direction of the net force on the sock, and determine its magnitude.

sock
●
Fnet = N
Support or Refute · Justify

C4. An appliance designer makes the following claim.

Claim: Increasing the spin speed of the clothes from 8.0 m/s to 16 m/s in the same drum would quadruple the centripetal force on each piece of clothing.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Multiple choice

C5. A smaller drum with half the radius spins clothes at the same speed. How does the centripetal acceleration change?

Constructed response

C6. A manufacturer wants a faster spin cycle. Identify one benefit and one drawback of increasing the drum’s spin speed.

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