Q: A 2 kg object is moving in a vertical circle of radius 1.5 m. What is the apparent weight at the bottom of the circle if its speed there is 5 m/s?

$$n = 2g + \frac{2 \times 25}{1.5}$$

Q: A CD spins at 10000 rpm. If its radius is 0.06 m, what is the speed of a point on its rim?

$$v = 2\pi r f = 2\pi \times 0.06 \times \frac{10000}{60}$$

Question 1

A car is moving around a flat, unbanked circular track of radius $$r. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed the car can have without skidding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$

Question 2

A satellite orbits the Earth at a height $$h$$ above the surface. Which equation gives the acceleration due to gravity at this height?

Accepted Answer

$$g = \frac{GM_e}{(R_e + h)^2$}$$

Question 3

A bucket of water is swung in a vertical circle of radius $$r. $$What is the minimum speed at the top of the circle so that the water does not fall out?

Accepted Answer

$$v_{min} = \sqrt{g r}$$

Question 4

Which of the following best describes the direction of centripetal acceleration for a particle in uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle.

Question 5

A 1 kg mass is attached to a string and swung in a horizontal circle of radius 2 m at a constant speed of 4 m/s. What is the tension in the string?

Accepted Answer

$$T = 16 N$$

Question 6

The period $$T of a $$satellite in a circular orbit of radius $$r$$ around a planet of mass $$M is $$given by:

Accepted Answer

$$T = 2\pi \sqrt{\frac{r^3$}{GM}}$$

Question 7

A particle moves in a circle of radius $$r$$ with constant angular velocity $$\omega. $$What is the magnitude of its linear velocity?

Accepted Answer

$$v = \omega r$$

Question 8

Which of the following statements about centrifugal force is correct?

Accepted Answer

It is a fictitious force that appears in a rotating reference frame.

Question 9

A 2 kg object is moving in a vertical circle of radius 1.5 m. What is the apparent weight at the bottom of the circle if its speed there is 5 m/s?

Accepted Answer

$$n = 2g + \frac{2 	imes 25}{1.5}$$

Question 10

The gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r is$$:

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 11

A CD spins at 10000 rpm. If its radius is 0.06 m, what is the speed of a point on its rim?

Accepted Answer

$$v = 2\pi r f = 2\pi 	imes 0.06 	imes \frac{10000}{60}$$

Question 12

If the angular position $$	heta of a $$particle is given by $$	heta = 2t^2$ (in radians), what is its angular velocity at t = 3$ s?

Accepted Answer

$$\omega = 12$$ rad/s

Question 13

A highway curve is banked at an angle $$	heta so $$that a car can round the curve of radius $$r$$ without friction. What is the correct expression for the speed?

Accepted Answer

$$v = \sqrt{g r 	an 	heta}$$

Question 14

Which of the following is true about the rtz-coordinate system in circular motion?

Accepted Answer

The r-axis points toward the center, the t-axis is tangent, and the z-axis is perpendicular to the plane.

Question 15

A satellite is in a circular orbit around Earth. If the radius of the orbit is doubled, how does the period change?

Accepted Answer

It increases by a factor of $$2^{3/2}$$

Question 16

Which of the following best explains why the measured value of $$g at $$Earth's surface is less than the value calculated from Newton's law of gravitation?

Accepted Answer

The rotation of the Earth reduces the apparent weight due to the required centripetal acceleration.

Question 17

A particle moves in a circle with non-uniform speed. Which of the following is true about its acceleration?

Accepted Answer

It has both radial (centripetal) and tangential components.

Question 18

The equivalence of inertial and gravitational mass is a fundamental property explained by:

Accepted Answer

Einstein's general theory of relativity

Motion in a Circle: Kinematics and Dynamics of Circular Motion

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