Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the time of flight $$T$$?

$$T = \frac{2 v_0$ \sin \theta}{g}$$

Question 1

A car accelerates from rest with a constant acceleration $$a$$ for a time $$t. $$What is the final velocity $$v of $$the car?

Accepted Answer

$$v = a t$$

Question 2

Which of the following correctly expresses the work done $$W by a $$constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta to $$the direction of the force?

Accepted Answer

$$W = F d \cos 	heta$$

Question 3

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed $$v at $$the bottom?

Accepted Answer

$$v = \sqrt{2 g h}$$

Question 4

Which of the following is the correct expression for the period $$T of a $$simple pendulum of length $$L$$?

Accepted Answer

$$T = 2 \pi \sqrt{\frac{L}{g}}$$

Question 5

A ball is thrown vertically upward with initial velocity $$v_0. $$What is the maximum height $$h_{max} it $$reaches?

Accepted Answer

$$h_{max} = \frac{v_0$^2}{2g}$$

Question 6

Which of the following is the correct formula for the moment of inertia $$I of a $$solid sphere of mass $$M$$ and radius $$R$$ about its center?

Accepted Answer

$$I = \frac{2}{5} M R^2$

Question 7

A force $$F is $$applied to a mass $$m$$ causing it to accelerate. According to Newton's second law, what is the acceleration $$a$$?

Accepted Answer

$$a = \frac{F}{m}$$

Question 8

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$

Question 9

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the time of flight $$T$$?

Accepted Answer

$$T = \frac{2 v_0$ \sin 	heta}{g}$$

Question 10

Which of the following is the correct expression for the kinetic energy $$K of a $$rotating object with moment of inertia $$I$$ and angular velocity $$\omega$$?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 11

A block of mass $$m is $$attached to a horizontal spring and oscillates with angular frequency $$\omega. $$What is the relationship between $$\omega$$, $$k$$, and $$m$$?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 12

A disk of mass $$M$$ and radius $$R$$ rotates about its central axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2} M R^2$

Question 13

A car of mass $$m$$ moves at velocity $$v. $$What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} m v^2$

Question 14

A satellite orbits Earth at a height where the acceleration due to gravity is $$g'. $$What is the orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{g' r}$$

Question 15

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

Accepted Answer

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

Question 16

A ball is dropped from a height $$h. $$How long does it take to reach the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 17

A car travels in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 18

A block slides across a rough surface and comes to rest due to friction. Which equation best describes the work done by friction?

Accepted Answer

$$W = -\mu_k m g d$$

Question 19

A solid cylinder of mass $$M$$ and radius $$R$$ rolls without slipping down an incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{\frac{2 g h}{1 + \frac{1}{2}}}$$

PHYS 1001H Formula Sheet: Core Concepts in College Physics

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