Science: Circular Motion and Centripetal Force Worksheet

Question 1

Define centripetal force in your own words and describe the direction it points during circular motion.

Accepted Answer

Centripetal force is the net force that keeps an object moving in a circular path. It always points toward the center of the circle.

Question 2

A 2 kg ball moves in a circle of radius 3 m at a speed of 6 m/s. Calculate its centripetal acceleration.

Accepted Answer

The centripetal acceleration is a = v^2 / r = 6^2 / 3 = 36 / 3 = 12 m/s^2. The ball's centripetal acceleration is 12 m/s^2 toward the center.

Question 3

A 2 kg ball moves in a circle of radius 3 m at a speed of 6 m/s. Calculate the centripetal force acting on it.

Accepted Answer

The centripetal force is F = mv^2 / r = 2 x 6^2 / 3 = 2 x 36 / 3 = 24 N. The net force is 24 N toward the center of the circle.

Question 4

A car travels around a flat circular track of radius 50 m at 10 m/s. If the speed doubles to 20 m/s and the radius stays the same, by what factor does the centripetal force change?

Accepted Answer

Centripetal force depends on the square of speed, so doubling the speed makes the force 2^2 = 4 times as large. The centripetal force increases by a factor of 4.

Question 5

A student swings a 0.5 kg rubber stopper in a horizontal circle of radius 0.8 m at a speed of 4 m/s. Calculate the centripetal force.

Accepted Answer

The centripetal force is F = mv^2 / r = 0.5 x 4^2 / 0.8 = 0.5 x 16 / 0.8 = 8 / 0.8 = 10 N. The force is 10 N toward the center.

Question 6

Explain why an object moving in a circle is accelerating even if its speed stays constant.

Accepted Answer

An object in circular motion is accelerating because its velocity is changing direction at every moment. Acceleration happens whenever velocity changes, even if the speed remains constant.

Question 7

A 1200 kg car rounds a curve of radius 40 m with a centripetal acceleration of 5 m/s^2. Find the net centripetal force on the car.

Accepted Answer

The net centripetal force is F = ma = 1200 x 5 = 6000 N. The car experiences a centripetal force of 6000 N toward the center of the curve.

Question 8

A satellite moves in a circular orbit because of gravity. Identify the force providing the centripetal force and explain its role.

Accepted Answer

Gravity provides the centripetal force for the satellite. This inward gravitational force continually changes the satellite's direction so it stays in orbit instead of moving in a straight line.

Question 9

A 3 kg object moves in a circle with radius 2 m and centripetal acceleration 18 m/s^2. Find its speed.

Accepted Answer

Use a = v^2 / r. Then v^2 = ar = 18 x 2 = 36, so v = 6 m/s. The object's speed is 6 m/s.

Question 10

Compare the centripetal force needed for two objects of the same mass moving at the same speed if one travels in a circle of radius 2 m and the other in a circle of radius 4 m.

Accepted Answer

Centripetal force is inversely proportional to radius when mass and speed stay the same. The object moving in the 2 m radius circle needs twice as much centripetal force as the object moving in the 4 m radius circle.

Question 11

A roller coaster car moves through a vertical loop. At the top of the loop, what direction must the centripetal force point, and why?

Accepted Answer

At the top of the loop, the centripetal force must point downward toward the center of the loop. It must point inward because centripetal force always acts toward the center of the circular path.

Question 12

A 1.5 kg mass moves in a circle of radius 0.75 m with a centripetal force of 18 N. Calculate its speed.

Accepted Answer

Use F = mv^2 / r. Then v^2 = Fr / m = 18 x 0.75 / 1.5 = 13.5 / 1.5 = 9, so v = 3 m/s. The speed of the mass is 3 m/s.

Science: Circular Motion and Centripetal Force

Science: Circular Motion and Centripetal Force

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