- #1

- 94

- 6

**Question 1:**

1. Homework Statement

1. Homework Statement

A bug of mass m crawls radially outwards with a constant speed v’ on a disc that

rotates with a constant angular velocity ω about a vertical axis. The speed v’ is relative to the

center of the disc. Assume a coefficient of static friction μ, find out where on the disc the bug

starts to slip.

## Homework Equations

F = ma = ΣF_i

## The Attempt at a Solution

The question asks when the force of friction is finally overcome, so I think:

ma = 0 = F_friction - F_cent.

Or

F_friction = F_cent.

μmg = (mv

^{2}/r)

v = wr

Solving for r:

r = (1/ω) √(2μg)

Seems too easy... Is this right?

**Question 2:**

1. Homework Statement

1. Homework Statement

A particle is placed on top of a smooth (frictionless) sphere of radius R. If the particle is slightly

disturbed, at what point will it leave the sphere?

## Homework Equations

Same as first question, just

F = ma = ΣF_i

## The Attempt at a Solution

Similarly, we want to know when the normal force of the sphere on the particle is overcome:

F_norm = F_cent

mg CosΘ = (mv

^{2}/r)

CosΘ = y/R (where

**y**is the height above the center of the sphere)

So:

y = v

^{2}/g

Finding v

^{2}:

Using conservation of energy, PE_initial = PE_final + KE_final

mgR = mgy + mv

^{2}/2

Solving for v

^{2}

v

^{2}= 2g(R-y)

Placing into equation for y:

y = 2g(R-y)/g = 2(R-y)

Solving for y:

y = (2/3) R

Correct? Or am I making a horrible mistake?