Question 1

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. If the amplitude of oscillation is doubled, what happens to the maximum kinetic energy of the mass?

Accepted Answer

It quadruples.

Question 2

A simple pendulum of length $$L is $$taken to the Moon, where the acceleration due to gravity is $$g_{moon} = 1.62\ \mathrm{m/s^2$}. If $$its period on Earth is $$T_{earth}$$, what is its period on the Moon?

Accepted Answer

$$T_{moon} = T_{earth} \sqrt{\dfrac{g_{earth}}{g_{moon}}}$$

Question 3

A satellite orbits Earth in a circular orbit of radius $$r. $$Which of the following correctly expresses the gravitational force acting on the satellite?

Accepted Answer

$$F = \dfrac{G M_{E} m}{r^2$}$$

Question 4

A 2 kg object is moving in a circle of radius 3 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$F = 8.0\ \mathrm{N}$$

Question 5

According to Kepler's third law, the square of the period $$T of a $$planet's orbit is proportional to which of the following?

Accepted Answer

The cube of the semi-major axis $$a of $$its orbit: $$T^2$$ \propto $$a^3$$

Question 6

A torque of $$12\ \mathrm{N \cdot m} is $$applied to a wheel with a moment of inertia $$I = 4\ \mathrm{kg \cdot m^2$}. $$What is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = 3\ \mathrm{$$rad/s^2$$}$$

Question 7

A figure skater pulls in her arms during a spin, reducing her moment of inertia to half its original value. If her initial angular velocity was $$\$$omega_0$$, what is her final angular velocity?

Accepted Answer

$$2\$$omega_0$$

Question 8

A solid sphere and a hollow sphere of equal mass and radius are released from rest at the top of an incline. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia.

Question 9

A 0.5 kg mass is attached to a string and swung in a horizontal circle of radius 2 m at a speed of 3 m/s. What is the tension in the string?

Accepted Answer

$$T = 9.0\ \mathrm{N}$$

Question 10

A planet has twice the mass and half the radius of Earth. What is the acceleration due to gravity on its surface compared to Earth?

Accepted Answer

It is 8 times greater.

Question 11

A disk rotates with constant angular acceleration. If its angular velocity increases from $$2\ \mathrm{rad/s} to$$ $$8\ \mathrm{rad/s} in 3 $$seconds, what is its angular acceleration?

Accepted Answer

$$2\ \mathrm{$$rad/s^2$$}$$

Question 12

A 5 kg object is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

$$v = 14\ \mathrm{m/s}$$

Question 13

A 0.2 kg mass attached to a spring oscillates with a period of 0.5 s. What is the spring constant $$k$$?

Accepted Answer

$$k = 6.32\ \mathrm{N/m}$$

Question 14

A child sits on a merry-go-round at a distance of 2 m from the center, rotating at 1 revolution every 4 seconds. What is the child's linear speed?

Accepted Answer

$$v = \pi\ \mathrm{m/s}$$

Question 15

A 3 kg mass moving at 4 m/s collides elastically with a stationary 2 kg mass. What is the velocity of the 3 kg mass after the collision?

Accepted Answer

$$v = 0.4\ \mathrm{m/s}$$

Question 16

A uniform rod of length $$L$$ and mass $$M$$ rotates about one end. What is its moment of inertia?

Accepted Answer

$$I = \dfrac{1}{3} M L^2$

Question 17

A 1 kg ball is attached to a string and swung in a vertical circle of radius 1.5 m. What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$v = 2.7\ \mathrm{m/s}$$

Question 18

A 0.5 kg mass moves in a circle of radius 0.2 m at an angular speed of $$10\ \mathrm{rad/s}. $$What is its angular momentum?

Accepted Answer

$$L = 1.0\ \mathrm{kg \cdot m^2$/s}$$

Question 19

A 2 kg object is moving at 5 m/s. What is its kinetic energy?

Accepted Answer

$$KE = 20\ \mathrm{J}$$

Question 20

A 0.3 kg mass attached to a spring oscillates with an amplitude of 0.1 m and a maximum speed of 2 m/s. What is the spring constant $$k$$?

Accepted Answer

$$k = 120\ \mathrm{N/m}$$

Physics Final Exam Study Guide: Key Topics and Concepts

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