Circular Motion

Circular Motion

Fill in the Blanks

Remember that acceleration involves a change in velocity. This can happen if either the speed or direction changes. In circular motion the direction of motion is continuously changing, so it is accelerating even if the speed is c..............

The acceleration is always towards the centre and is called ..................... acceleration.

Fill in the Blanks

The faster it goes, or the faster it changes direction = greater centripetal acceleration.

The bigger the radius, or the slower it changes direction =

centripetal acceleration)

(as speed increases, centripetal acceleration increases)

(as radius increases, centripetal acceleration decreases)

Fill in the Blanks

If we want to make something accelerate we need to apply a force

This is called centripetal force and must be in the same d

as the centripetal acceleration.

Multiple Select

The equations that relate centripetal force and acceleration to velocity:

• $F_c=\frac{mv^2}{r}$

• $a_c=\frac{v^2}{r}$

• $a_c=\frac{mv^2}{r}$

• $F_c=\frac{v^2}{r}$

Multiple Choice

A 0.50 g ant is clinging precariously to a spinning turntable. The turntable’s radius is 20cm and it is spinning at 40 rpm.

a) Calculate the period of the turntable.

b) Calculate the ant’s velocity.

c) Calculate the centripetal force on the ant.

• a) T = 1.5s b) 0.84 ms^-1 c) F_c = 1.8 x 10^-3 N

• a) T = 0.67s b) 1.9 ms^-1 c) F_c = 2.1 x 10^-4 N

• a) T = 1.5s b) 1.2 ms^-1 c) F_c = 2.1 x 10^-3 N

Explain why the water doesn’t come out of the bucket as it swings in a vertical circle.

Fill in the Blanks

The reason is that the centripetal acceleration of the

is greater than 9.8 ms^-2 thus it is accelerating down at a greater rate than the water falls due to gravity. So even as the water falls it stays together with the bucket since it is falling at a greater rate.

Banked curves on roads are designed to aid cornering by provideing an extra force component to accerlerate the car towards the centre of the turn...

Multiple Choice

A 2500kg bus is turning a corner at 150ms^-1 and is banked at an angle of 10⁰. a) Calculate the size of the centripetal force.

b) Calculate the radius of the turn.

• a) F_c = 800 N b) r = 3 000 m

• a) F_c = 4400 N b) r = 13 000 m

• a) F_c = 40 N b) r = 1000 m

Multiple Choice

What is the force that causes centripetal acceleration when a car goes around a curve on a flat road?

• Friction

• Gravity

• Normal

• Tension

Multiple Choice

When a ball attached to string is swung in a vertical circle

• the tension is always equal to the centripetal force
• the tension is greatest at the top
• the tension is greatest at the bottom
• the tension is greatest halfway up

Multiple Choice

The maximum speed with which a car can take a circular turn of radius R is v. The maximum speed with which the same car, under the same conditions, can take a circular turn of radius 2R is

• 2v

• v√2

• 4v

• 2v√2

Multiple Choice

A popular daredevil trick is to complete a vertical loop on a motorcycle. This trick is dangerous, however, because if the motorcycle does not travel with enough speed, the rider falls off the track before reaching the top of the loop. What is the minimum speed necessary for a rider to successfully go around a vertical loop of 10 meters?

• 5.5 ms^-1

• 9.9 ms^-1

• 4.4 ms^-1

• 8.8 ms^-1